Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, conduct a test of each of the independent variables. Are there any that should be dropped?

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, develop a histogram of the residuals and a normal probability plot. Are there any problems?

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, determine the variance inflation factor for each of the independent variables. Are there any problems?

Solve for $x$ by writing the equation in exponential form.

$$\log _4 x=-2$$

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, draw a scatter diagram comparing sales volume with each of the independent variables. Comment on the results.

Following are two income statements for Alexis Co. for the year ended December 31. The left number column is prepared before any adjusting entries are recorded, and the right column includes the effects of adjusting entries. The middle column shows a blank space for each income statement effect of the eight adjusting entries a through g (the balance sheet part of the entries is not shown here). Analyze the statements and prepare the eight adjusting entries a through g that likely were recorded. Note: Answer for a has two entries (i) of the $7,000 adjustment for Fees Earned, 30% (or$2,100) has been earned but not billed, and (ii) the other 70% (or $4,900) has been earned by performing services that were paid for in advance.$

$$\begin{matrix} \text{ALEXIS CO. Income Statements For Year Ended December 31}\\ & \text{Unadjusted} & \text{Adjustments} & \text{Adjusted}\\ \text{Revenues }\\ \text{Fees earned} \ldots\ldots\ldots & \text{\$18,000} & \text{a} & \text{\$25,000}\\ \text{Commissions earned} \ldots\ldots\ldots & \text{36,500} & \quad & \text{36,500}\\ \text{Total revenues} \ldots\ldots\ldots & \text{54,500} & \quad & \text{61,500}\\ \text{Expenses} \ldots\ldots\ldots \\ \text{Depreciation expense—Computers} \ldots\ldots\ldots & \text{0} & \text{b} & \text{1,600}\\ \text{Depreciation expense—Office furniture} \ldots\ldots\ldots & \text{0} & \text{c} & \text{1,850}\\ \text{Salaries expense} \ldots\ldots\ldots & \text{13,500} & \text{d} & \text{15,750}\\ \text{Insurance expense} \ldots\ldots\ldots & \text{0} & \text{e} & \text{1,400}\\ \text{Rent expense} \ldots\ldots\ldots & \text{3,800} & \quad & \text{3,800}\\ \text{Office supplies expense} \ldots\ldots\ldots & \text{0} & \text{f} & \text{580}\\ \text{Advertising expense} \ldots\ldots\ldots & \text{2,500} & \quad & \text{2,500}\\ \text{Utilities expense} \ldots\ldots\ldots & \text{1,245} & \text{f} & \text{1,335}\\ \text{Total expenses} \ldots\ldots\ldots & \text{21,045} & \quad & \text{28,815}\\ \text{Net income} \ldots\ldots\ldots & \text{\$33,455} & \quad & \text{\$32,685}\\ \end{matrix}$$

$

PrintTech, Inc. is introducing a new line of ink-jet printers and would like to promote the number of pages a user can expect from a print cartridge. A sample of 10 cartridges revealed the following number of pages printed.

The demographics of nine counties in an Atlantic seaboard state's eastern section are being researched by a regional planner. She's compiled the following information:

$$\begin{array}{|cccc|} \hline \text { County } & \text { Median Income } & \text { Median Age } & \text { Coastal}^* \\ \hline \text { A } & \$ 48,157 & 57.7 & 1 \\ \text { B } & 48,568 & 60.7 & 1 \\ \text { C } & 46,816 & 47.9 & 1 \\ \text { D } & 34,876 & 38.4 & 0 \\ \text { E } & 35,478 & 42.8 & 0 \\ \text { F } & 34,465 & 35.4 & 0 \\ \text { G } & 35,026 & 39.5 & 0 \\ \text { H } & 38,599 & 65.6 & 0 \\ \text { J } & 33,315 & 27.0 & 0 \\ { }^* 1=\text { yes, } 0=\text { no. } & & & \\ \hline \end{array}$$

Using this, test each of the individual coefficients to see if they are significant.

Consider the ANOVA table that follows. Analysis of Variance

$$\begin{array}{lrrrr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & F \\ \text { Regression } & 5 & 3710.00 & 742.00 & 12.89 \\ \text { Residual Error } & 46 & 2647.38 & 57.55 & \\ \text { Total } & 51 & 6357.38 & & \end{array}$$

a. Determine the standard error of estimate. About $95 \%$ of the residuals will be between what two values? b. Determine the coefficient of multiple determination. Interpret this value. c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom.

A sample of General Mills employees was studied to determine their degree of satisfaction with their quality of life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage

$$(X_1)$$

, annual income

$$(X_2)$$

, number of children living

$$(X_3)$$

, value of all assets

$$(X_4)$$

, status of health in the form of an index

$$(X_5)$$

, and the average number of social activities per week—such as bowling and dancing

$$(X_6).$$

Suppose the multiple regression equation is: Ŷ=

$$16.24 + 0.017X_1 + 0.0028X_2 + 42X_3 + 0.0012X_4 + 0.19X_5 + 26.8X_6$$

a. What is the estimated index of satisfaction for a person who first married at 18, has an annual income of $26,500, has three children living, has assets of$156,000, has an index of health status of 141, and has 2.5 social activities a week on the average? b. Which would add more to satisfaction, an additional income of $10,000 a year or two more social activities a week?

Using Exercise 16, determine the .95 prediction interval, in thousands of dollars, for a particular salesperson who makes 40 contacts.

On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was $80 \%$. The standard error of estimate was 10 . There were 20 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam.

Refer to Exercise . The regression equation is $\hat{y}=29.29-0.96 x$, the sample size is 8 , and the standard error of the slope is 0.22 . Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?

Can the population of an urban area be estimated without taking a census? In Geographical Analysis (Jan. 2007) geography professors at the University of Wisconsin at Milwaukee and Ohio State University demonstrated the use of satellite image maps in estimating urban population. A portion of Columbus, Ohio, was partitioned into n = 125 census block groups, and satellite imagery was obtained. For each census block, the following variables were measured: population density ( y ), proportion of block with low-density residential areas

$$(x_1),$$

and proportion of block with high-density residential areas

$$(x_)$$

A first-order model for y was fitted to the data and produced the following results:

$$\hat { y } = - .0304 + 2.006 x _ { 1 } + 5.006 x _ { 2 } , R ^ { 2 } = .686$$

a. Give a practical interpretation of each

$$\beta \text { -estimate }$$

in the model. b. Give a practical interpretation of the coefficient of determination,

$$R^2.$$

c. State

$$H_0 \ and \ H_a$$

for a test of the overall adequacy of the model. d. Refer to part c . Compute the value of the test statistic. e. Refer to parts c and d . Make the appropriate conclusion at

$$\alpha = .01$$