Simple Regression 2-10-12

8/13/2019 Simple Regression 2-10-12

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CHAPTER 16 SECTION 3-4: SIMPLE LINEAR REGRESSION AND

CORRELATION

MULTIPLE CHOICE

88. In a simple linear regression problem, the following sum of squares are produced: ,

, and . The percentage of the variation inythat is explained by the

variation inxis:a. 2!b. "!c. ##!d. $!

%&': ( )T': * +-: 'TI/& *0.#1*0.

83. In simple linear regression, most often we perform a two1tail test of the population slope *to

determine whether there is sufficient evidence to infer that a linear relationship exists. The nullhypothesis is stated as:a. H$: *4 $

b. H$: *4 b*c. H$: *$

d. &one of these choices.

%&': % )T': * +-: 'TI/& *0.#1*0.

3$. Testing whether the slope of the population regression line could be 5ero is equivalent to testingwhether the:a. sample coefficient of correlation could be 5erob. standard error of estimate could be 5eroc. population coefficient of correlation could be 5erod. sum of squares for error could be 5ero

%&': )T': * +-: 'TI/& *0.#1*0.

3*. 6iven that and n4 0, the standard error of estimate is:

a. #,"3.$$b. 3#".2c. #$.0*d. &one of these choices.

%&': )T': * +-: 'TI/& *0.#1*0.

32. The symbol for the population coefficient of correlation is:a. rb.

c. r2

d. 2

%&': ( )T': * +-: 'TI/& *0.#1*0.

This edition is intended for use outside of the 7.'. only, with content that may be different from the 7.'. dition. This may not be resold,copied, or distributed without the prior consent of the publisher.


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3#. 6iven that the sum of squares for error is 0$ and the sum of squares for regression is *$, then thecoefficient of determination is:a. $.23b. $.#$$c. $."$$d. &one of these choices.

%&': )T': * +-: 'TI/& *0.#1*0.

3. % regression line using 2 observations produced ''+ 4 **8.08 and '' 4 0.#2. The standard errorof estimate was:a. 2.**b. *.0c. 2.d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

3. The symbol for the sample coefficient of correlation is:a. rb.

c. r2

d. 2

%&': % )T': * +-: 'TI/& *0.#1*0.

30. 6iven the least squares regression line , and a coefficient of determination of $.8*,

the coefficient of correlation is:a. $.00

b. $.8*c. $.3$

d. $.3$%&': )T': * +-: 'TI/& *0.#1*0.

3". 6iven the least squares regression line , and a coefficient of determination of $.8*, the

coefficient of correlation is:a. $.00

b. $.8*c. $.3$

d. $.3$

%&': )T': * +-: 'TI/& *0.#1*0.

38. If the coefficient of determination is $.3", then which of the following is true regarding the slope ofthe regression line9a. %ll we can tell is that it must be positive.b. It must be $.3".c. It must be $.38".d. annot tell the sign or the value.

%&': )T': * +-: 'TI/& *0.#1*0.



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33. In regression analysis, if the coefficient of determination is *.$, then:a. the sum of squares for error must be *.$b. the sum of squares for regression must be *.$c. the sum of squares for error must be $.$d. the sum of squares for regression must be $.$

%&': )T': * +-: 'TI/& *0.#1*0.

*$$. The coefficient of correlation is used to determine:a. the strength and direction of the linear relationship betweenxandy.b. the least squares estimates of the regression parameters.c. the predicted value ofyfor a given value ofx.d. %ll of these choices.

%&': % )T': * +-: 'TI/& *0.#1*0.

*$*. If the coefficient of correlation is $.8$, then the percentage of the variation in ythat is explained by

the variation inxis:a. 8$!

b. 0!c. 83!d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

*$2. If all the points in a scatter diagram lie on the least squares regression line, then the coefficient ofcorrelation must be:a. *.$b. *.$

c. either *.$ or *.$

d. $.$

%&': )T': * +-: 'TI/& *0.#1*0.

*$#. If the coefficient of correlation is $.0$, then the coefficient of determination is:

a. $.0$

b. $.#0

c. $.#0d. $.""

%&': )T': * +-: 'TI/& *0.#1*0.

*$. If the coefficient of correlation betweenxandyis close to *.$, this indicates that:a. ycausesxto happen.

b. xcausesyto happen.c. both a and b.d. there may or may not be a causal relationship betweenxandy.

%&': )T': * +-: 'TI/& *0.#1*0.



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*$. hen all the actual values ofyare equal to their predicted values, the standard error of estimate willbe:a. *.$b. *.$

c. $.$d. &one of these choices.

%&': )T': * +-: 'TI/& *0.#1*0.

*$0. hich of the following statistics and procedures can be used to determine whether a linear modelshould be employed9a. The standard error of estimate.b. The coefficient of determination.c. The t1test of the slope.d. %ll of these choices are true.

%&': )T': * +-: 'TI/& *0.#1*0.

*$". In testing the hypotheses:H$: *4 $ vs.H$: * $, the following statistics are available: ,

, , , and . The value of the test statistic is:a. 2.$2b. $.#$0c. *.$

d. $.#$$

%&': % )T': * +-: 'TI/& *0.#1*0.

*$8. The standard error of estimatesis given by:

a.

b.

c.d.

%&': )T': * +-: 'TI/& *0.#1*0.

*$3. If the standard error of estimates4 2$ and n4 *$, then the sum of squares for error, '', is:

a. $$b. #,2$$c. ,$$$d. $,$$$

%&': ( )T': * +-: 'TI/& *0.#1*0.

**$. The smallest value that the standard error of estimatescan assume is:

a. *

b. $c. *d.

%&': ( )T': * +-: 'TI/& *0.#1*0.



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***. If cov;x, y< 4 *20$, , and , then the coefficient of determination is:

a. $.3$b. *.2#c. $.8*d. $.$$0

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**2. The standard error of estimatesis a measure of the:

a. variation ofyaround the regression line.b. variation ofxaround the regression line.c. variation ofyaround the mean .

d. variation ofxaround the mean .

%&': % )T': * +-: 'TI/& *0.#1*0.

**#. The )earson coefficient of correlation r equals one when there is no:a. linear relationship betweenxandy.b. unexplained variation.

c. y1intercept in the model.d. slope in the model.

%&': ( )T': * +-: 'TI/& *0.#1*0.

**. In regression analysis, the coefficient of determinationR2measures the amount of variation in ythat is:a. caused by the variation inx.b. explained by the variation inx.c. unexplained by the variation inx.d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

**. If we are interested in determining whether two variables are linearly related, it is necessary to:a. perform the t1test of the slope *.

b. perform the t1test of the coefficient of correlation .

c. either a or b since they are identical.d. &one of these choices.

%&': )T': * +-: 'TI/& *0.#1*0.

**0. In a regression problem the following pairs of ;x,y< are given: ;#, *


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**". In a regression problem, if the coefficient of determination is $.3, this means that:a. 3! of theyvalues are positive.b. 3! of the variation inycan be explained by the variation inx.c. 3! of theyvalues are predicted correctly by the model.d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

**8. The sample correlation coefficient betweenxandyis $.#". It has been found out that thep1value is

$.20 when testingH$:4 $ against the two1sided alternativeH*:$. To testH$:4 $ against the

one1sided alternativeH*:> $ at a significant level of $.*3#, thep-value will be equal to

a. $.*28b. $.*2c. $."d. $.8"2

%&': % )T': * +-: 'TI/& *0.#1*0.

**3. In simple linear regression, which of the following statements indicates there is no linear relationship

between the variablesxandy9a. oefficient of determination is *.$.

b. oefficient of correlation is $.$.c. 'um of squares for error is $.$.d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

*2$. If the sum of squared residuals is 5ero, then the:a. coefficient of determination must be *.$.b. coefficient of correlation must be *.$.c. linear relationship betweenxandyis perfect.d. %ll of these choices are true.

%&': )T': * +-: 'TI/& *0.#1*0.

*2*. If the standard error of estimate is 5ero, then:a. the coefficient of determination must be *.$.b. all the points fall on the regression line.c. there is no unexplained variation left.d. %ll of these choices are true.

%&': )T': * +-: 'TI/& *0.#1*0.

*22. The standard error of the estimate is a measure of the:

a. total variation in theyvariable.b. variation around the regression line.c. percentage of variation inyexplained by the variation inx.d. the variation of thexvariable.

%&': ( )T': * +-: 'TI/& *0.#1*0.



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*2#. In simple linear regression, the coefficient of correlation rand the least squares estimate b*of the

population slope *:

a. must be equal.b. must have the same sign.c. are not related.d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

*2. In performing a regression analysis which of the following must be true about the distribution of theerror variable9a. The distribution is normal with mean 5ero.b. The errors associated with oneyvalue are independent of errors associated with anothery

value.c. The standard deviation is constant for each value ofx.d. %ll of these choices are true.

%&': )T': * +-: 'TI/& *0.#1*0.

*2. hich of the following assumptions concerning the probability distribution of the random error term isstated incorrectly9a. The distribution is normal.b. The mean of the distribution is $.c. The variance of the distribution increases asxincreases.d. The errors are independent from one value ofyto the next.

%&': )T': * +-: 'TI/& *0.#1*0.

*20. In a simple linear regression problem, rand b0:a. must be equal to each other.b. must have the same sign.c. must have opposite signs.

d. are not related.

%&': ( )T': * +-: 'TI/& *0.#1*0.

*2". If the coefficient of correlation is $.3$, then the percentage of the variation in the dependent variableythat is explained by the variation in the independent variablexis:a. 3$!b. 8*!c. 3!d. &one of these choices.

%&': ( )T': * +-: 'TI/& *0.#1*0.

TRUE/FALSE

*28. If the value of the sum of squares for error '' equals 5ero, then the coefficient of determination mustequal 5ero.

%&': - )T': * +-: 'TI/& *0.#1*0.



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*23. hen the actual valuesyof a dependent variable and the corresponding predicted values are the

same, the standard error of the estimate will be *.$.

%&': - )T': * +-: 'TI/& *0.#1*0.

*#$. The value of the sum of squares for regression ''+ can never be smaller than $.$.

%&': T )T': * +-: 'TI/& *0.#1*0.

*#*. The value of the sum of squares for regression ''+ can never be smaller than *.

%&': - )T': * +-: 'TI/& *0.#1*0.

*#2. If the coefficient of correlation is *.$, then the coefficient of determination must be *.$.

%&': T )T': * +-: 'TI/& *0.#1*0.

*##. In a simple linear regression model, testing whether the slope *of the population regression line could

be 5ero is the same as testing whether or not the population coefficient of correlation equals 5ero.

%&': T )T': * +-: 'TI/& *0.#1*0.

*#. hen the actual valuesy of a dependent variable and the corresponding predicted values are the

same, the standard error of estimateswill be $.$.

%&': T )T': * +-: 'TI/& *0.#1*0.

*#. If there is no linear relationship between two variablesxandy, the coefficient of determination must

be *.$.

%&': - )T': * +-: 'TI/& *0.#1*0.

*#0. The value of the sum of squares for regression ''+ can never be larger than the value of sum ofsquares for error ''.

%&': - )T': * +-: 'TI/& *0.#1*0.

*#". In a simple linear regression problem, the least squares line is , and the coefficient of

determination is $.8*. The coefficient of correlation must be $.3$.

%&': - )T': * +-: 'TI/& *0.#1*0.

*#8. In simple linear regression, the denominator of the standard error of estimatesis .

%&': T )T': * +-: 'TI/& *0.#1*0.

*#3. The value of the sum of squares for regression ''+ can never be larger than the value of total sum ofsquares ''T.

%&': T )T': * +-: 'TI/& *0.#1*0.



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*$. If the coefficient of determination is *.$, then the coefficient of correlation must be *.$.

%&': - )T': * +-: 'TI/& *0.#1*0.

**. orrelation analysis is used to determine whether there is a linear relationship between an independentvariablexand a dependent variabley.

%&': T )T': * +-: 'TI/& *0.#1*0.

*2. If the coefficient of correlation is $.8*, then the percentage of the variation in ythat is explained by

the regression line is 8*!.

%&': - )T': * +-: 'TI/& *0.#1*0.

*#. If all the points in a scatter diagram lie on the least squares regression line, then the coefficient ofcorrelation must be *.$.

%&': - )T': * +-: 'TI/& *0.#1*0.

*. The probability distribution of the error variable is normal, with meanE;< 4 $, and standarddeviation 4*.

%&': - )T': * +-: 'TI/& *0.#1*0.

*. If the coefficient of determination is $.3, this means that 3! of the variation in the independentvariablexcan be explained by theyvariable.

%&': - )T': * +-: 'TI/& *0.#1*0.

*0. If the coefficient of determination is $.3, this means that 3! of theyvalues were predicted correctlyby the regression line.

%&': - )T': * +-: 'TI/& *0.#1*0.

*". If the error variable is normally distributed, the test statistic for testingH$: *4 $ has a 'tudent t1

distribution with n2 degrees of freedom.

%&': T )T': * +-: 'TI/& *0.#1*0.

*8. The coefficient of determination is equal to the coefficient of correlation squared.

%&': T )T': * +-: 'TI/& *0.#1*0.

*3. % 5ero correlation coefficient between a pair of random variables means that there is no linearrelationship between the random variables.

%&': T )T': * +-: 'TI/& *0.#1*0.

*$. % 5ero population correlation coefficient forx andymeans that there is no type of relationshipwhatsoever betweenx andy.

%&': - )T': * +-: 'TI/& *0.#1*0.



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**. % store manager gives a pre1employment examination to new employees. The test is scored from * to*$$. ?e has data on their sales at the end of one year measured in dollars. ?e wants to @now if there isany linear relationship between pre1employment examination score and sales. %n appropriate test touse is the t1test of the population correlation coefficient.

%&': T )T': * +-: 'TI/& *0.#1*0.

COMPLETION

*2. -or a regression analysis to be valid, the error variable must have a;n< AAAAAAAAAAAAAAAAAAAAdistribution.

%&': normal

)T': * +-: 'TI/& *0.#1*0.

*#. -or a regression analysis to be valid, the error variable must have a mean of AAAAAAAAAAAAAAAAAAAA.

%&':5ero$

)T': * +-: 'TI/& *0.#1*0.

*. -or a regression analysis to be valid, the error variable must have a standard deviation that isAAAAAAAAAAAAAAAAAAAA regardless of the value ofx.

%&':constantthe same

)T': * +-: 'TI/& *0.#1*0.

*. -or a regression analysis to be valid, the value of the error variable associated with any particularvalue ofyis AAAAAAAAAAAAAAAAAAAA of the value of the error variable associated with any other valueofy.

%&': independent

)T': * +-: 'TI/& *0.#1*0.

*0. If the standard error of estimate is AAAAAAAAAAAAAAAAAAAA, this implies that the modelBs fit is poor.

%&':largebig

)T': * +-: 'TI/& *0.#1*0.



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*". The unbiased estimator of the variance of the error variable is found by ta@ing

AAAAAAAAAAAAAAAAAAAA divided by n2.

%&':''sum of squares for error

)T': * +-: 'TI/& *0.#1*0.

*8. If the regression line is hori5ontal, then we conclude thatyAAAAAAAAAAAAAAAAAAAA ;is=is not< relatedtox.

%&': is not

)T': * +-: 'TI/& *0.#1*0.

*3. If the regression line is hori5ontal, the slope is AAAAAAAAAAAAAAAAAAAA andxandyare not related.

%&':5ero$

)T': * +-: 'TI/& *0.#1*0.

*0$. The degrees of freedom for the test statistic for the slope is AAAAAAAAAAAAAAAAAAAA.

%&':

n2

n2

)T': * +-: 'TI/& *0.#1*0.

*0*. The coefficient of AAAAAAAAAAAAAAAAAAAA measures the amount of variation in the dependentvariable that is explained by the variation in the independent variable.

%&': determination

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SHORT ANSWER

Car Speed ad Ga! M"#ea$e

%n economist wanted to analy5e the relationship between the speed of a car ;x< and its gas mileage ;y


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*02. Dar 'peed and 6as Cileage &arrativeE alculate the standard error of estimate, and describe whatthis statistic tells you about the regression line.

%&':

s4 *.8F the model fits the data well.

)T': * +-: 'TI/& *0.#1*0.

*0#. Dar 'peed and 6as Cileage &arrativeE oes this data provide sufficient evidence at the !significance level to infer that a linear relationship exists between speed and gas mileage9

%&':

H$:4 $ vs.H*:$

+eGection region: H tH > t$.$2,*$4 2.228

Test statistic: t4 3."

onclusion: +eGect the null hypothesis. There is sufficient evidence at the ! significance level toinfer that a linear relationship exists between speed and gas mileage. %s speed increases, gas mileagedecreases.

)T': * +-: 'TI/& *0.#1*0.

*0. Dar 'peed and 6as Cileage &arrativeE )redict with 33! confidence the gas mileage of a cartraveling mph.

%&':

#*.2#0 0.28. Thus, 4 2.32, and 7 4 #".2.

)T': * +-: 'TI/& *0.#1*0.

*0. Dar 'peed and 6as Cileage &arrativeE alculate the )earson coefficient of correlation.

%&':

r4 $.3"

)T': * +-: 'TI/& *0.#1*0.

*00. Dar 'peed and 6as Cileage &arrativeE hat does the coefficient of correlation tell you about thedirection and strength of the relationship between the two variables9

%&':There is a very strong negative linear relationship between car speed and gas mileage. %s speedincreases, gas mileage decreases, and this relationship is very reliable.

)T': * +-: 'TI/& *0.#1*0.

*0". Dar 'peed and 6as Cileage &arrativeE alculate the coefficient of determination and interpret itsvalue.

%&':R24 $.3. This means that 3! of the total variation in gas mileage can be explained by the speed ofthe car.



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)T': * +-: 'TI/& *0.#1*0.

*08. The following *$ observations of variablesxandy were collected.

x * 2 # 0 " 8 3 *$

y 2 22 2* *3 * * *2 *$ 0 2

a. alculate the standard error of estimate.b. Test to determine if there is enough evidence at the ! significance level to indicate thatx

andy are negatively linearly related.c. alculate the coefficient of correlation, and describe what this statistic tells you about the

regression line.

%&':a. s4 *.#22

b. H$: *4 $ vs.H$: *J $

+eGection region: tJ t$.$,84 *.80

Test statistic: t 4 *0.$2

onclusion: +eGect the null hypothesis. There is enough evidence at the ! significancelevel to indicate thatx andy have a negative linear relationship, according to this data. %sspeed increases, gas mileage decreases.

c. r 4 $.38. This indicates a very strong negative linear relationship between the two

variables.

)T': * +-: 'TI/& *0.#1*0.

*03. onsider the following data values of variablesx andy.

x 2 0 8 *$ *#

y " ** *" 2* 2" #0

a. alculate the coefficient of determination, and describe what this statistic tells you aboutthe relationship between the two variables.

b. alculate the )earson coefficient of correlation. hat sign does it have9 hy9c. hat does the coefficient of correlation calculated tell you about the direction and

strength of the relationship between the two variables9

%&':a. R24 $.33. This means that 33.! of the variation in the dependent variableyis explained

by the variation in the independent variablex.b. r4 $.33". It is positive since the slope of the regression line is positive.c. There is a very strong ;almost perfect< positive linear relationship between the two

variables.

)T': * +-: 'TI/& *0.#1*0.



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S%!&"e ad S'" Ca(er

% medical statistician wanted to examine the relationship between the amount of sunshine ;x< andincidence of s@in cancer ;y


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%&':There is a very strong ;almost perfect< positive linear relationship between these two variables.

)T': * +-: 'TI/& *0.#1*0.

Sa#e! ad E)per"e(e

The general manager of a chain of furniture stores believes that experience is the most important factorin determining the level of success of a salesperson. To examine this belief she records last monthBssales ;in K*,$$$s< and the years of experience of *$ randomly selected salespeople. These data arelisted below.

'alesperson Lears of xperience 'ales

* $ " 2 2 3 # *$ 2$ # * 8 *8 0 * " *2 2$ 8 " *" 3 2$ #$*$ * 2

*". D'ales and xperience &arrativeE etermine the standard error of estimate and describe what thisstatistic tells you about the regression line.

%&':

s4 *."2F the model is a good fit for the data.

)T': * +-: 'TI/& *0.#1*0.

*"0. ;'ales and xperience &arrativeE etermine the coefficient of determination and discuss what itsvalue tells you about the two variables.

%&':R24 $.3#0, which means that 3.#0! of the variation in sales is explained by the variation in years ofexperience of the salesperson.

)T': * +-: 'TI/& *0.#1*0.

*"". D'ales and xperience &arrativeE alculate the )earson correlation coefficient. Interpret this result.

%&':r4 $.3"0. It has a positive sign since the slope of the regression line ;b*4 *.$8*"< is positive. Thisindicates a strong, positive linear relationship between years of experience and sales.

)T': * +-: 'TI/& *0.#1*0.



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*"8. D'ales and xperience &arrativeE onduct a test of the population coefficient of correlation todetermine at the ! significance level whether more experience is related to higher sales, as themanager speculates.

%&':

H$:4 $ vs.H*:>$

+eGection region: t> t.$,84 *.80Test statistic: t4 *2.8#onclusion: +eGect the null hypothesis. %ccording to this data, there is sufficient evidence to say thatas experience increases, sales increases.

)T': * +-: 'TI/& *0.#1*0.

*"3. D'ales and xperience &arrativeE onduct a test of the population slope to determine at the !significance level whether a positive linear relationship exists between years of experience and sales.

%&':

H$: *4 $ vs.H*: *>$

+eGection region: t> t.$,84 *.80Test statistic: t4 *2.8#onclusion: +eGect the null hypothesis. Les, a linear relationship exists between years of experienceand sales. %s experience increases, sales increases, according to this data.

)T': * +-: 'TI/& *0.#1*0.

*8$. D'ales and xperience &arrativeE o the tests ofand *in the previous two questions provide the

same results9 xplain.

%&':LesF both tests have the same value of the test statistic, the same reGection region, and of course the

same conclusion. This is not a coincidenceF the two tests are identical.

)T': * +-: 'TI/& *0.#1*0.

Ga*e W""$! + Ed%(a,"

%n ardent fan of television game shows has observed that, in general, the more educated thecontestant, the less money he or she wins. To test her belief she gathers data about the last eightwinners of her favorite game show. 'he records their winnings in dollars and the number of years ofeducation. The results are as follows.

ontestant Lears of ducation innings

* ** "$2 * $$# *2 0$$ *0 #$ ** 8$$0 *0 #$$" *# 0$8 * $$



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*8*. D6ame innings M ducation &arrativeE etermine the standard error of estimate and describe whatthis statistic tells you about the regression line.

%&':

s4 3.#3F the model fits the data well.

)T': * +-: 'TI/& *0.#1*0.

*82. D6ame innings M ducation &arrativeE etermine the coefficient of determination and discuss whatits value tells you about the two variables.

%&':R24 $.3*8, which means that 3*.8! of the variation in TN game showsB winnings is explained bythe variation in years of education.

)T': * +-: 'TI/& *0.#1*0.

*8#. D6ame innings M ducation &arrativeE alculate the )earson correlation coefficient. hat signdoes it have9 hy9

%&':

r4 $.38. It has a negative sign since the slope of the regression line ;b*4 83.*00"< is negative.

This means as education increases, winnings decreases, according to this data.

)T': * +-: 'TI/& *0.#1*0.

*8. D6ame innings M ducation &arrativeE onduct a test of the population coefficient of correlation todetermine at the ! significance level whether a negative linear relationship exists between years ofeducation and TN game showsB winnings.

%&':

H$:4 $ vs.H*:


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)T': * +-: 'TI/& *0.#1*0.

*80. D6ame innings M ducation &arrativeE o the tests and *in the previous two questions provide

the same results9 xplain.

%&':Les. This is not a coincidenceF the two tests are identical.

)T': * +-: 'TI/& *0.#1*0.

M."e Re.e%e!

% financier whose specialty is investing in movie productions has observed that, in general, movieswith Obig1nameO stars seem to generate more revenue than those movies whose stars are less well@nown. To examine his belief he records the gross revenue and the payment ;in K millions< given tothe two highest1paid performers in the movie for ten recently released movies.

Covie ost of Two ?ighest )aid 6ross +evenue)erformers ;Kmil< ;Kmil$

+eGection region:t> t$.$,84 *.80Test statistic: t 4 23.#$onclusion: +eGect the null hypothesis. % positive linear relationship exists between payment to thetwo highest1paid performers and gross revenue, according to this data.

)T': * +-: 'TI/& *0.#1*0.

*32. DCovie +evenues &arrativeE o the and *tests in the previous questions provide the same results9

xplain.

%&':LesF both tests have the same value of the test statistic, the same reGection region, and ofcourse the same conclusion. This is not a coincidenceF the two tests are identical.

)T': * +-: 'TI/& *0.#1*0.

C!, 0'!

The editor of a maGor academic boo@ publisher claims that a large part of the cost of boo@s is the costof paper. This implies that larger boo@s will cost more money. %s an experiment to analy5e the claim,a university student visits the boo@store and records the number of pages and the selling price oftwelve randomly selected boo@s. These data are listed below.



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(oo@ &umber of )ages 'elling )rice ;K$

+eGection region: t> t.$,*$4 *.8*2Test statistic: t 4 *2.28*

onclusion: +eGect the null hypothesis. %ccording to this data, we can infer at the ! significancelevel that the editor is correct. %s pages increase, selling price of the boo@ increases.

)T': * +-: 'TI/& *0.#1*0.

W"##"e Ne#! C(er,

%t a recent illie &elson concert, a survey was conducted that as@ed a random sample of 2$ peopletheir age and how many concerts they have attended since the first of the year. It is suspected thatolder concert goers tend to go to more of his concerts in one year than younger concert goers. The dataand analysis are shown below.

%ge 02 " $ 3 0" # 0 *&umber of oncerts 0 # 2 0 # *

%ge 8 0$ 3 0# 03 $ #8 2

&umber of oncerts # 2 2 * #



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%n xcel output follows:

*3. Dillie &elson oncert &arrativeE etermine the standard error of estimate and describe what thisstatistic tells you about the modelBs fit.

%&':

s4 $.3#3", and since the sample mean , we would have to admit that the standard error of

estimate is not very small. /n the other hand, it is not a large number either. (ecause there is no

predefined upper limit ons, it is difficult in this problem to assess the model in this way. ?owever,

using other criteria, the fit of the model is reasonable.

)T': * +-: 'TI/& *0.#1*0.

*30. Dillie &elson oncert &arrativeE etermine the coefficient of determination and discuss what itsvalue tells you about the two variables.

%&':R24 $.0#20, which means that 0.#20! of the variation in number of concerts attended is explainedby the variation in age of the attendees.

)T': * +-: 'TI/& *0.#1*0.

*3". Dillie &elson oncert &arrativeE alculate the )earson correlation coefficient and interpret.

%&':r4 $.8$2$. It has a positive sign since the slope of the regression line, b*, is positive. This says thereis a strong positive linear relationship between age of the concert attendee and the number of concertsthey have been to in a year.

)T': * +-: 'TI/& *0.#1*0.



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*38. Dillie &elson oncert &arrativeE onduct a test of the population coefficient of correlation todetermine at the ! significance level whether a positive linear relationship exists between age andnumber of concerts attended.

%&':

H$:4 $ vs.H*:>$

+eGection region: t> t.$,*84 *."#

Test statistic:

onclusion: +eGect the null hypothesis. Les, we can infer that at the ! significance level that apositive linear relationship exists between age and number of concerts attended in one year, accordingto this data.

)T': * +-: 'TI/& *0.#1*0.

*33. Dillie &elson oncert &arrativeE onduct a test of the population slope to determine at the !significance level whether a positive linear relationship exists between age and number of concertsattended.

%&':H$: *4 $ vs.H*: *>$

+eGection region: t> t.$,*84 *."#Test statistic: t4 .03"*onclusion: +eGect the null hypothesis. Les, we can infer that at the ! significance level that apositive linear relationship exists between age and number of concerts attended in one year, accordingto this data.

)T': * +-: 'TI/& *0.#1*0.

2$$. Dillie &elson oncert &arrativeE o the and *tests in the previous two questions provide the

same results9 xplain.

%&':LesF both tests have the same value of the test statistic, the same reGection region, and ofcourse the same conclusion. This is not a coincidenceF the two tests are identical.

)T': * +-: 'TI/& *0.#1*0.

O"# %a#",2 ad Pr"(e

Puality of oil is measured in %)I gravity degrees11the higher the degrees %)I, the higher the quality.The table shown below is produced by an expert in the field who believes that there is a positiverelationship between quality and price per barrel.



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/il degrees %)I )rice per barrel ;in K

Simple Regression 2-10-12

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