Chapter 4, Problem 17PT1

a.

To determine

To explain: Whether the weekly sales revenue is related to the length of the house assigned to the brand of house.

Answer to Problem 17PT1

No

Explanation of Solution

Given:

Figure is:

  

Output is:

  

From the provided scatter plot, the pattern in the plot is linear and positive. Also, the points are not deviating from the general pattern and outliers are not present in the plot. Thus, it could be said that the weekly sales revenue is related to the length of the house assigned to the brand of house.

b.

To determine

To find: The equation of the regression line.

Answer to Problem 17PT1

The equation is $\widehat{y}=317.94+152.680x$

Explanation of Solution

Calculation:

The general equation of regression line is,

  $\widehat{y}=a+bx$

According to the question, the dependent variable ( X ) is the shelf length and the dependent variable ( Y ) is the sales.

From the provided output, the constant value is 317.94 and the coefficient of the variable “Shelf length” is $317.94$ . Thus, $a=318.16$ and $152.680$ .

Putting the values of a and b in the regression line. Thus:

  $\begin{array}{c}\widehat{y}=a+bx\\ =317.94+152.680x\end{array}$

Thus, the regression line is $\widehat{y}=317.94+152.680x$ .

c.

To determine

To find: The best estimate of weekly sales revenue.

Answer to Problem 17PT1

The best estimate is $1081.34.

Explanation of Solution

Calculation:

The best estimate of weekly sales revenue can be calculated as:

  $\begin{array}{c}\widehat{y}=317.94+152.680x\\ =317.94+152.68\left(5\right)\\ =1081.34\end{array}$

Thus, the best estimate is $1081.34.

d.

To determine

To interpret: The value of s .

Explanation of Solution

From the output, s is 22.9212. It shows that on an average the predicted sale of the week is likely to be deviated by $22.9212 from the actual or true sale.

e.

To determine

To find: The coefficient of determination and interpret it

Explanation of Solution

The coefficient of determination shows the variation that is explained by the predictor variable on the response variable. Here, coefficient of determination is 98.2%

Thus, it shows that that the 98.2% of the variation on the response variable is explained by the least square line

f.

To determine

To provide: The sufficient explanation for the question of the manage related to the intercept.

Explanation of Solution

It could be seen that the range of the data is lying between 3 and 6 feet. Thus, it would be inappropriate if it is said that the length of the shelf is 0. Thus, the appropriate answer should be given by him.