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Vocabulary Calculator Calculations Dobbert’s Doozies

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Row 1, Col 1

Describe the difference betweenresidual and deviation.

Cite appropriatenotation.

Residual is the distance between the data y value and the predicted y value.

Deviation is the difference between the data y value and the average y value. y – “y hat”

1,2

Make a scatter plot of the data. State the type of function that models the data set. Be prepared to share with the class.

X 1 2 3 6 7 8 9 10Y 10643 4776 2194 637 483 371 298 222

Exponential

1,3

Make a scatter plot of the data. State the type of function thatmodels the data set. Find the Regression equaiton.

X 100 200 500 700 1000Y 60 46 31 26 21

Power or exponential

1,4

Describe the difference between

interpolation and extrapolation.

Interpolation corresponds with a value within the domain of the data set.

Extrapolation corresponds with a value outside the domain of the data set.

2,1

What information does r and r 2 provide us?

What vocabulary term is associated with r and r 2 ?

R is the correlation coefficient and describes the trend of the data, positive or negative, strong or weak. R2 is the coefficient of determination and describes the percent of variability of the data accounted for by the regression equation.

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−1 ≤ r ≤1

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0 ≤ r2 ≤1

2,2

Find the appropriate regressionequation for the set of data.

X 10 14 16 20 25 26 30Y 30 40 46 54 60 63 70

Y = 1.924x + 13.089

2,3

Use lists on your calculator to find.SSdev Be prepared to share with the class.

X 10 14 16 20 25 26Y 30 40 46 54 60 63

792.833

2,4

Algebraically find the logarithmic equation that contains the points (2,10) and (8,15).

7.5 + 3.607lnx = y

3,1

Define centroid.What is its significance with respect to a

linear regression equation?

The centroid is the point defined by (x-average, y-average). It is the point that always lies on the linear regression equation.

3,2

Make a residual plot to determine if a linear or exponential equation better models the data set.

X 0 2 4 6 8 10Y .07 .2 .6 2 5 16

Exponential

3,3

Given the data set, calculate the coefficient of determination. Use the definition that includes SSres

and SSdev.X 2 4 6 8 10 12Y 10 17 21 28 35 38

0.990

3,4

Describe the numerical patterns that describe linear, power, exponential, and logarithmic

functions.

linear add-addpower multiply-multiplyexponential add-multiplylogarithmic multiply-add.

4,1

Using sigma notation, write an Expression that express the sum of

the square of the residuals.

(Type the question for 4,1 here.)?

4,2

Based on the linear residual plot, isa linear model a good fit for the data? Support your claim.

Yes…the points possess a random pattern.

4,3

Find the power and exponential regression equations. Paste the equations into y1 and y2.Create residual plots for the power and exponential models. Determine which modelis a better fit.X 3 4 5 6 7 8 9 10 11Y 46 41 36 31 27 24 21 18 15

(Type the question for 4,3 here.)?

4,4

State the date and time of the mathExam.

Tuesday, December 18 @ 10:20

5,1

Write the expression that calculatesThe coefficient of determination.

R2 = (SSdev - SSres )/SSdev

5,2

Based on the logarithmic residualplot, is a logarithmic model a goodFit for the data? Support yourclaim.

No, the plot indicated there is a function with a better fit. The plot has a non-random pattern.

5,3

Find the linear and exponential regression equations. Paste the equations into y1 and y2.Create residual plots for the linear and exponential models. Determine which modelis a better fit.

X 3 4 5 6 7 8 9 10 11Y 23 37 50 62 76 89 102 114 126

Linear

5,4

Data has been entered into lists 1 and 2,describe the rule to calculateState the rule for list 3 and any other Calculator instructions needed.

L3 = (L2 – mean(L2))2

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y − y( )∑ 2