Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 2, Problem 144E
(a)
To determine
To graph: The
(a)
Expert Solution
Explanation of Solution
Graph: To draw the scatterplot for the provided data set, the below steps are followed in Minitab software.
Step 1: Open the “MEIS” file in Minitab software.
Step 2: Go to Graph
Step 3: Choose the option “Simple” and click “OK”.
Step 4: Select “Sales” as Y variables and “Dwellpermit” as X variables.
Step 5: Click “OK” twice.
The scatterplot is obtained as:
To determine
To explain: The relationship between the variables and the presence of the outliers.
Expert Solution
Answer to Problem 144E
Solution: Though the relationship between the variables is very weak, but there is no outlier in the data set.
Explanation of Solution
The scatterplot obtained in part (a) shows that the data are very much scattered. That is there is very weak relationship between the response variable sales and the explanatory variable, issued permits. But there is no outlier present in the data set.
(b)
To determine
To find: The least-squares regression line for the data.
(b)
Expert Solution
Answer to Problem 144E
Solution: The least-squares regression line is obtained as
Explanation of Solution
Calculation: To draw the regression line and obtain the sketch of the regression line, the below steps are followed in the Minitab software.
Step 1: Right click on the obtained graph in the part (a).
Step 2: Go to Add
Step 3: Click on “Linear” under the menu “Model Order” and tick the “Fit intercept”.
Step 4: Click on “OK” to obtain the regression line.
The obtained regression equation is
Graph: The below graph shows the regression line.
(c)
To determine
To explain: The slope of the obtained line.
(c)
Expert Solution
Answer to Problem 144E
Solution: The slope can be interpreted as if there is an increase of 1unit of the variable, issued permit for dwelling then there is an increase of 0.1263 units in the value of the variable sales.
Explanation of Solution
The slope of the least-square regression line indicates the amount of increase (decrease) in the response variable due to the 1-unit increase (decrease) in the value of the explanatory variable. In the provided equation, the amount of increase in the value of the response variable, sales is 0.1263 due to the 1-unit increase in the value of the variable issued permit for dwelling.
(d)
To determine
To explain: The intercept of the line.
(d)
Expert Solution
Answer to Problem 144E
Solution: The intercept can be interpreted as the value of the response variable when the value of the explanatory variable is zero. As the value of the response variable is 109.8 for the zero issued permits, it is appropriate to use the intercept for explaining the relationship between the variables.
Explanation of Solution
The intercept of the least-squares linear regression provided the value of the response variable when the value of the explanatory variable is zero. The explanatory variable can be zero because the index of issued permits for new dwelling can be zero and the value of the response variable for zero issued permit is 109.8. Therefore, it is appropriate to use the intercept for explaining the relationship between the variables.
(e)
To determine
The sales for an index of 224 dwelling permits.
(e)
Expert Solution
Answer to Problem 144E
Solution: The predicted value of the sales is 138.0912.
Explanation of Solution
The predicted value of the sales can be obtained by substituting the value of the index of dwelling permit in the least-squares linear regression equation.
The predicted value can be calculated as:
(f)
To determine
To find: The residual value for Canada.
(f)
Expert Solution
Answer to Problem 144E
Solution: The obtained value of the residual is
Explanation of Solution
Calculation: The sale for the Canada is provided as 122. The residual value for the sales for Canada whose index of dwelling permits is 224 is calculated as:
(g)
To determine
The percentage of variability in sales is explained by dwelling permit.
(g)
Expert Solution
Answer to Problem 144E
Solution: The explained percentage of variability in sales is 10.30%.
Explanation of Solution
The variability is explained by r 2 r 2
Therefore, the proportion of variation that is explained by the explanatory variables of the model is 10.30%.
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Chapter 2 Solutions
Introduction to the Practice of Statistics
Ch. 2.1 - Prob. 1UYKCh. 2.1 - Prob. 2UYKCh. 2.1 - Prob. 3UYKCh. 2.1 - Prob. 4UYKCh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.2 - Prob. 10UYK
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