Practice Problems: Chapter 12

(part E is worth 3 points–all other parts

of the question are worth 1 point)

1) A)

Provide detailed

reasoning why or why not Regression is appropriate using just the scatterplot

and correlation given below.

.png”>

Correlations:

Taxes, size (Taxes in dollars, size in

square feet)

Pearson

correlation of Taxes and size = 0.738

P-Value = 0.000

B) Given the Regression Equation below indicate the explanatory

variable and the response variable.

Regression

Analysis: Taxes versus size

The regression

equation is

Taxes = – 372 +

1.34 size

C) What is the

y-intercept? Does the y-intercept have

any logical interpretation? We cannot

logically interpret the y-intercept unless we have data points at X = 0 in the

data set. If in fact we cannot

logically interpret the y-intercept, then the y-intercept is only useful for

positioning the line properly in the plot.

So, the question hinges on whether we have data points at X=0 in the

data set.

Regression

Analysis: Taxes versus size

The regression

equation is

Taxes = – 372 +

1.34 size

D) What is the slope coefficient?

What is the slope interpretation?

Be specific (ie: for each unit increase in ____, we expect

_____ to increase/decrease by _____).

Regression

Analysis: Taxes versus size

The regression

equation is

Taxes = – 372 +

1.34 size

E)What is the

predicted Tax value for a house of size 2,000 square feet? Show all work.

Regression

Analysis: Taxes versus size

The regression

equation is

Taxes = – 372 +

1.34 size

F) From the output below can we conclude that size is a significant

linear predictor of real estate taxes?

In answering this question, first provide the null and alternative

hypothesis being tested. Then,

calculate the test statistic using the values in the output (show all

work). Finally, indicate the p-value of

our test statistic and the conclusion and reasoning behind your conclusion.

Predictor Coef

SE Coef T P

Constant -372.2

200.6 -1.86 0.067

size 1.3368

0.1235 10.82 0.000

S = 684.635 R-Sq = 54.5% R-Sq(adj) = 54.0%

G) The R2value is 54.5%. Provide a detailed description of what an R2

of 54.5% indicates.

H) What are the FIT (fitted values) and what are the RESI

(Residuals)? Be specific.

I) Describe why we use a Residuals vs Fitted Values scatterplot to

test for constant variance. (see figure

12.4 in the text) Remember, the fitted

values (the values on the line) are the mean Y values for the given X value and

we expect the observed Y values to be equally distributed around each and every

X value.

J) Given the Residuals vs Fitted values scatterplot below is the

constant variance assumption appropriate?

.png”>

K) Why do we want the Residuals to be

normally distributed?

Given the Probability Plot below are these

Residuals normally distributed?

.png”>

L)

Given the X value of 2,500 square feet–you are given a 95% confidence

interval for ?y and a prediction interval. What do each of these indicate?

Predicted Values

for New Observations

New

Obs Fit

SE Fit 95% CI 95% PI

1

2969.8 138.4 (2695.2, 3244.5) (1583.7, 4356.0)

Values of

Predictors for New Observations

New

Obs size

1 2500

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