Chapter 4, Problem AP1.17CPT

(a)

To determine

To describe the relationship between length and sales.

Explanation of Solution

Direction: It is positive because the pattern in the scatter plot slopes upwards.

Form: It is linear because there is no strong curvature present in the scatter plot.

Strength: It is strong because the points in the scatter plot do not deviate much from the general pattern in the points.

Unusual features: There are no outliers because there appear to be no points that deviate strongly from the general pattern in the data.

Thus there is strong, positive and linear relationship between shelf length and sales.

(b)

To determine

To write the equation of least square regression line.

Answer to Problem AP1.17CPT

  $\widehat{y}=317.94+152.680x$ .

Explanation of Solution

Let:

x =Shelf length

y =Sales

General equation is $\widehat{y}=a+bx$ of the regression line.

The y -intercept is given in the row “Constant” and in the column “Coef” of the given table:

  $a=317.94$

The slope b is given in the row “Shelf length” and in the column “Coef” of the given table:

  $b=152.680$

We then obtain:

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

(c)

To determine

To find out what is the best estimate of the weekly sales revenue.

Answer to Problem AP1.17CPT

The best estimate is $1081.34$ .

Explanation of Solution

It is given that:

  $\widehat{y}=317.94+152.680x$

Thus, at $x=5$ :

  $\begin{array}{l}\widehat{y}=317.94+152.680x\\ =317.94+152.680(5)\\ =1081.34\end{array}$

  $x=5$ since they are looking weekly revenue sales.

Thus the best estimate is $1081.34$ .

(d)

To determine

To interpret the value of s .

Answer to Problem AP1.17CPT

  $s=22.9212$

Explanation of Solution

The standard deviation of the residual is given after “S=” in the computer output:

  $s=22.9212$

The standard deviation of the residual is the average discrepancy between the observed y -values and the predicted y - values.

On average, the predicted sales deviate by $22.9212$ dollars from the actual sales.

(e)

To determine

To identify and interpret the coefficient of determination.

Answer to Problem AP1.17CPT

  $r^2=98.2\%$ .

Explanation of Solution

The coefficient of determination is:

  $r^2=98.2\%$

  $98.2\%$ of the variation in the amount of sales in dollars can be accounted for by the LSRL that is dependent upon the shelf length in feet.