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.
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?
K) Why do we want the Residuals to be
normally distributed?
Given the Probability Plot below are these
Residuals normally distributed?
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
