Introduction to Statistics: Chapter 14
Homework (Inference for
Regression)Correct 100%
14.1
A professor tells his class that he knows their second exam score without their having to
take the test. He tells them that the second exam score can be predicted from the first
with this equation: Predicted second exam score=5+0.75 (first exam score)
This tells us that the deterministic part of the regression model that predicts second
exam score on the basis of first exam score is a straight line. What factor might
contribute to the random component? In other words, why might a student's score not
fall exactly on this line? - ANSWER The amount of time the student could study
A doctor says he can predict the height (in inches) of a child between 2 and 9 years old
from the child's age (in years) by using the following equation.: Predicted
Height=31.78+2.45 Age
This tells us that the deterministic part of the regression model. What factors might
contribute to the random component? In other words, why might a child's height not fall
exactly on this line? - ANSWER Diet
The table shows the height (in feet) and the number of floors for five particular buildings.
The regression model for predicting the height from the number of floors is shown
below. Use the table and the regression model to complete parts (a) and (b) below.
Predicted Height=476+4 × (Number of Floors)
Floors: 75, 88, 74, 57, 59
Height: 879, 829, 735, 706 - ANSWER a. Find the predicted values.
Ans: Floors: 75, 88, 74, 57, 59
Predicted Height: 776, 828, 772, 704, 712
b. Find the residuals. (Remember that if the actual value is less than the predicted
value, the residual will have a negative sign.)
Ans: Floors: 75, 88, 74, 57, 59
Residual: 103, 1, −37, 2, 14
NOTE: Actual - Predictual = Residual
Figure 1 shows a scatterplot of the price and age of a random sample of used cars and
includes the regression line. Figure 2 shows a residual plot based on the regression
, line. Complete a and b below. - ANSWER a. Is the linear regression model appropriate
for these data? Explain.
Ans: The residual plot shows that the trend is not a straight line, so the linear condition
fails. The linear model is not appropriate.
b. How old is the car that is farthest from the regression line?
Ans: The farthest car from the regression line is 6 years old.
NOTE: Look at Figures 1 and Figures 2!
Figure 1 shows a scatterplot for the number of semesters that students have attended a
community college and the number of credits they have accumulated. Figure 2 shows a
residual plot of the same data. These are linked below. Is the linear regression model
appropriate for these data? Why or why not? Assume the observations are
independently measured. - ANSWER The standard deviation condition does not hold,
so the linear model is not appropriate.
NOTE: Look at Figures 1 and Figures 2!
Figure A shows a scatterplot of the current salary (in thousands of dollars per year) and
the beginning salary of many employees at one company. Figure B shows a residual
plot of the same data. Is linear regression appropriate for these data? Why or why not? -
ANSWER Ans: The linear regression model is inappropriate for these data because
there is evidence that the constant SD condition is not met.
NOTE: View the scatterplot and residual plot of employee salaries!
Figure 1 shows a scatterplot of wages of twins for a group of 68 pairs of twins. Figure 2
shows a residual plot of the same data. Figure 3 shows a QQ plot of these residuals. Is
the linear regression model appropriate for these data? Why or why not? Assume the
observations are independently measured. - ANSWER Is the linear regression model
appropriate for these data? Why or why not?
Ans: The residual plot shows an increasing trend, and the QQ plot does not follow a
straight line. Linear regression is inappropriate for this data set, because the linearity
condition and the Normality condition fail.
14.2
The statistics for the test that the intercept is 0 can be found in the row labeled
"Constant." Find the test statistic.
Ans: t=2.21
Find the p-value for the test.
Ans: The p-value is .0342.
Homework (Inference for
Regression)Correct 100%
14.1
A professor tells his class that he knows their second exam score without their having to
take the test. He tells them that the second exam score can be predicted from the first
with this equation: Predicted second exam score=5+0.75 (first exam score)
This tells us that the deterministic part of the regression model that predicts second
exam score on the basis of first exam score is a straight line. What factor might
contribute to the random component? In other words, why might a student's score not
fall exactly on this line? - ANSWER The amount of time the student could study
A doctor says he can predict the height (in inches) of a child between 2 and 9 years old
from the child's age (in years) by using the following equation.: Predicted
Height=31.78+2.45 Age
This tells us that the deterministic part of the regression model. What factors might
contribute to the random component? In other words, why might a child's height not fall
exactly on this line? - ANSWER Diet
The table shows the height (in feet) and the number of floors for five particular buildings.
The regression model for predicting the height from the number of floors is shown
below. Use the table and the regression model to complete parts (a) and (b) below.
Predicted Height=476+4 × (Number of Floors)
Floors: 75, 88, 74, 57, 59
Height: 879, 829, 735, 706 - ANSWER a. Find the predicted values.
Ans: Floors: 75, 88, 74, 57, 59
Predicted Height: 776, 828, 772, 704, 712
b. Find the residuals. (Remember that if the actual value is less than the predicted
value, the residual will have a negative sign.)
Ans: Floors: 75, 88, 74, 57, 59
Residual: 103, 1, −37, 2, 14
NOTE: Actual - Predictual = Residual
Figure 1 shows a scatterplot of the price and age of a random sample of used cars and
includes the regression line. Figure 2 shows a residual plot based on the regression
, line. Complete a and b below. - ANSWER a. Is the linear regression model appropriate
for these data? Explain.
Ans: The residual plot shows that the trend is not a straight line, so the linear condition
fails. The linear model is not appropriate.
b. How old is the car that is farthest from the regression line?
Ans: The farthest car from the regression line is 6 years old.
NOTE: Look at Figures 1 and Figures 2!
Figure 1 shows a scatterplot for the number of semesters that students have attended a
community college and the number of credits they have accumulated. Figure 2 shows a
residual plot of the same data. These are linked below. Is the linear regression model
appropriate for these data? Why or why not? Assume the observations are
independently measured. - ANSWER The standard deviation condition does not hold,
so the linear model is not appropriate.
NOTE: Look at Figures 1 and Figures 2!
Figure A shows a scatterplot of the current salary (in thousands of dollars per year) and
the beginning salary of many employees at one company. Figure B shows a residual
plot of the same data. Is linear regression appropriate for these data? Why or why not? -
ANSWER Ans: The linear regression model is inappropriate for these data because
there is evidence that the constant SD condition is not met.
NOTE: View the scatterplot and residual plot of employee salaries!
Figure 1 shows a scatterplot of wages of twins for a group of 68 pairs of twins. Figure 2
shows a residual plot of the same data. Figure 3 shows a QQ plot of these residuals. Is
the linear regression model appropriate for these data? Why or why not? Assume the
observations are independently measured. - ANSWER Is the linear regression model
appropriate for these data? Why or why not?
Ans: The residual plot shows an increasing trend, and the QQ plot does not follow a
straight line. Linear regression is inappropriate for this data set, because the linearity
condition and the Normality condition fail.
14.2
The statistics for the test that the intercept is 0 can be found in the row labeled
"Constant." Find the test statistic.
Ans: t=2.21
Find the p-value for the test.
Ans: The p-value is .0342.
