Chapter 9.4, Problem 5P

(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 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 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 variable that has the largest spread of data values relative to its mean.

Explain why the variable that has large coefficient of variation could be expected to change a lot relative to its average value.

Explain why variable $x_1$ has the smallest coefficient of variation even when it has largest standard deviation with the help of mean.

(b)

To determine

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

Find the coefficient of determination $r^2$ for each pair of variables.

Find the variable (other than $x_1$) that has the least influence on box office receipts on $x_1$.

Find the percent of the variation in box office receipts can be attributed to the corresponding variation in production costs.

(c)

To determine

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

(d)

To determine

Find the regression equation.

Find the expected for the corresponding change in $x_1$ (box office receipts) if $x_2$ (production costs) and $x_4$ (book sales) were held fixed but $x_3$ (promotional costs) was increased by $1 million.

(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.

Explain why book sales $x_4$ probably are not contributing much information in the regression model to forecast box office receipts $x_1$.

(f)

To determine

Find a 90% confidence interval for the coefficient $x_2$.

Find a 90% confidence interval for the coefficient $x_3$.

Find a 90% confidence interval for the coefficient $x_4$.

(g)

To determine

Find the predicted value for first-year box office receipts when production costs were $x_2=11.4$ million, promotion costs were $x_3=4.7$ million and book sales were $x_4=8.1$ million.

Find the 85% confidence range for the predicted value for first-year box office receipts when production costs were $x_2=11.4$ million, promotion costs were $x_3=4.7$ million and book sales were $x_4=8.1$ million.

(h)

To determine

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

Find the predicted value for budgeted for promotion costs when projected box office sales $x_1=100$ million; production costs were $x_2=12$ million and book sales were $x_4=9.2$ million.

Find the 85% confidence range for the predicted value for budgeted for promotion costs when projected box office sales $x_1=100$ million; production costs were $x_2=12$ million and book sales were $x_4=9.2$ million.