b. Find the mean and variance of Y.

(10%) (2) The data shown below were taken from a $3 \times 2$ factorial experiment to examine the effects of factor A (keyboard configuration, 3 levels) and factor B (word processing package, 2 levels) on typing speed. Each cell consists of the times needed for each of 4 randomly assigned keyboardists to type a standard document under each set of conditions (in minutes). Factor B | Factor A | 1 | 2 | | --- | --- | --- | | 1 | 26 19 20 21 | 24 21 20 23 | | 2 | 30 24 25 29 | 33 27 31 29 | | 3 | 26 22 27 17 | 31 23 24 26 | Given SSA=184.33, SSB=28.17, SSAB=8.33, SST=405.83 a. Create the ANOVA table.

b. Test at the \(5\%\) significance level to determine if time differences exist among the different keyboard configurations.

(10%) (3) Assume you have noted the following prices for books and the number of pages that each book contains. | Book | Pages (x) | Price (y) | | --- | --- | --- | | A | 500 | $7.00 | | B | 700 | 7.50 | | C | 750 | 9.00 | | D | 590 | 6.50 | | E | 540 | 7.50 | | F | 650 | 7.00 | | G | 480 | 4.50 | | Sample mean | 601.43 | 7.00 | | Sample standard deviation | 102.54 | 1.35 | | Sample variance | 10514.29 | 1.83 | | Sample covariance (x, y) | 104.17 | | a. Develop a least-squares estimated regression line.

b. Develop a \(90\%\) confidence interval for estimating the average price of books that contain 800 pages.

(20%)(4) The following results were obtained from a multiple regression analysis of supermarket profitability. The dependent variable, y, is the profit (in thousands of dollars) and the independent variables, x1 and x2, are the food sales and nonfood sales (also in thousands of dollars). | | ANOVA Table | | | --- | --- | --- | | | df | SS | | Regression | - | 562 | | Residual | 9 | 225 | | Total | | | | | Coefficients | Standard Error | | --- | --- | --- | | Intercept | -15.06 | | | x1 | 0.10 | 0.05 | | x2 | 0.25 | 0.09 | a. Write the estimated regression equation for the relationship between the variables.

b. Compute the multiple coefficient of determination and fully interpret its meaning.

c. Carry out a test to determine whether \( y \) is significantly related to the independent variables. Use a .05 level of significance.

d. Carry out a test to determine if there is a significant relationship between \( x_{1} \) and \( y \). Use a .05 level of significance.

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