(Use SPSS) A random sample of nine male race horses at a Fauquier County stable yielded the following data on age of horse (months) and time to run a mile (seconds). Age of Horse (x) 22 27 62 47 38 ☐32 55 50 58 Time to Run a Mile (y) 96 102 158 125 113 107 142 139 141 a. Construct a scatterplot of the data. What does it suggest about the relationship between the age and speed of male race horses in Fauquier County? b. Assuming that the simple linear regression model is appropriate, obtain the equation of the estimated regression line. c. What percentage of the observed variation in Time to Run a Mile can be explained by the resulting model? d. Check the regression assumptions using a normal probability plot of the residuals and a plot of the explanatory variable values versus the studentized residuals. e. A race horse trainer in Fauquier County claimed that there is a useful linear relationship between the two variables. Do you agree? Carry out a formal hypothesis test to support your answer at the 5% significance level. f. Give an estimate of the average change in Time to Run a Mile associated with a one month increase in Age of Horse (i.e., x increases by 1 unit). Use an appropriate 95% interval. g. Give an estimate of the specific Time to Run a Mile for Dr. Street's horse, "Jamaica Mistaica", that is 54 months old, and do so in a way that incorporates an appropriate 95% interval.
(Use SPSS) A random sample of nine male race horses at a Fauquier County stable yielded the following data on age of horse (months) and time to run a mile (seconds). Age of Horse (x) 22 27 62 47 38 ☐32 55 50 58 Time to Run a Mile (y) 96 102 158 125 113 107 142 139 141 a. Construct a scatterplot of the data. What does it suggest about the relationship between the age and speed of male race horses in Fauquier County? b. Assuming that the simple linear regression model is appropriate, obtain the equation of the estimated regression line. c. What percentage of the observed variation in Time to Run a Mile can be explained by the resulting model? d. Check the regression assumptions using a normal probability plot of the residuals and a plot of the explanatory variable values versus the studentized residuals. e. A race horse trainer in Fauquier County claimed that there is a useful linear relationship between the two variables. Do you agree? Carry out a formal hypothesis test to support your answer at the 5% significance level. f. Give an estimate of the average change in Time to Run a Mile associated with a one month increase in Age of Horse (i.e., x increases by 1 unit). Use an appropriate 95% interval. g. Give an estimate of the specific Time to Run a Mile for Dr. Street's horse, "Jamaica Mistaica", that is 54 months old, and do so in a way that incorporates an appropriate 95% interval.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
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Transcribed Image Text:(Use SPSS) A random sample of nine male race horses at a Fauquier County stable yielded the following data on age of horse (months) and time to run a mile (seconds).
Age of Horse (x)
22
27
62
47
38
☐32
55
50
58
Time to Run a Mile (y)
96
102
158
125
113
107
142
139
141
a. Construct a scatterplot of the data. What does it suggest about the relationship between the age and speed of male race horses in Fauquier County?
b. Assuming that the simple linear regression model is appropriate, obtain the equation of the estimated regression line.
c. What percentage of the observed variation in Time to Run a Mile can be explained by the resulting model?
d. Check the regression assumptions using a normal probability plot of the residuals and a plot of the explanatory variable values versus the studentized residuals.
e. A race horse trainer in Fauquier County claimed that there is a useful linear relationship between the two variables. Do you agree? Carry out a formal hypothesis
test to support your answer at the 5% significance level.
f. Give an estimate of the average change in Time to Run a Mile associated with a one month increase in Age of Horse (i.e., x increases by 1 unit). Use an appropriate 95%
interval.
g. Give an estimate of the specific Time to Run a Mile for Dr. Street's horse, "Jamaica Mistaica", that is 54 months old, and do so in a way that incorporates an appropriate
95% interval.
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