Chapter 9.4, Problem 6P

(a)

To determine

Find the mean for $x_1$.

Find the mean for $x_2$.

Find the mean for $x_3$.

Find the mean for $x_4$.

Find the mean for $x_5$.

Find the mean for $x_6$.

Find the standard deviation for $x_1$.

Find the standard deviation for $x_2$.

Find the standard deviation for $x_3$.

Find the standard deviation for $x_4$.

Find the standard deviation for $x_5$.

Find the standard deviation for $x_6$.

Find the coefficient of variation for $x_1$.

Find the coefficient of variation for $x_2$.

Find the coefficient of variation for $x_3$.

Find the coefficient of variation for $x_4$.

Find the coefficient of variation for $x_5$.

Find the coefficient of variation for $x_6$.

Find the variable that has the greatest spread of data values relative to its mean.

Find the variable that has the smallest spread of data values relative to its mean.

(b)

To determine

Find the sample correlation coefficient r for each pair of variables.

Find the coefficient of determination $r^2$ for all pairs involving variable $x_1$.

Find the variable (other than $x_1$) that has the greatest influence on annual net sales $x_1$.

Find the variable (other than $x_1$) that has the least influence on annual net sales $x_1$.

(c)

To determine

Find the percentage of the variation in $x_1$ can be explained by the corresponding variations in $x_2$, $x_3$, $x_4$, $x_5$ and $x_6$ taken together.

(d)

To determine

Find the regression equation.

Find the expected value for the corresponding change in annual net sales, if two new competing stores moved into the sales district but the other explanatory variables did not change.

Find the expected value for the corresponding change in annual net sales, if increased the local advertising by a thousand dollars but the other explanatory variables did not change.

(e)

To determine

Test whether the coefficient of $x_2$ is different from zero or not.

Test whether the coefficient of $x_3$ is different from zero or not.

Test whether the coefficient of $x_4$ is different from zero or not.

Test whether the coefficient of $x_5$ is different from zero or not.

Test whether the coefficient of $x_6$ is different from zero or not.

(f)

To determine

Find the predicted value for annual net sales when $x_2=2.8$, $x_3=250$, $x_4=3.1$, $x_5=7.3$, and $x_6=2$.

Find the 85% confidence range for the predicted value for annual net sales when $x_2=2.8$, $x_3=250$, $x_4=3.1$, $x_5=7.3$, and $x_6=2$.

(g)

To determine

Find the regression model with $x_4$ as the response variable and $x_1$, $x_2$, $x_3$, $x_5$ and $x_6$ as explanatory variables.

Find the predicted value for advertising costs when $x_1=163$, $x_2=2.4$, $x_3=188$, $x_5=6.6$, and $x_6=10$.

Find the 80% confidence range for the predicted value for advertising costs when $x_1=163$, $x_2=2.4$, $x_3=188$, $x_5=6.6$, and $x_6=10$.

Find the range of advertising costs is appropriate for this store.