# DAT 565 Practice Week 5 Exercise

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1. An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 26 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.03 bushels.

(a) Find the approximate width of a 95% prediction interval for wheat yield. (Round your answer to 2 decimal places.)

(b) Find the approximate width using the quick rule. (Round your answer to 2 decimal places.)

(c) The quick rule gives a similar result.

2)         In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees.

(a) Write the fitted regression equation.

(b-1) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (Round t.025 to 3 decimal places.)

(b-2) Choose the correct option for H0:β1 = 0 vs H1:β1 ≠ 0.

(c-1) Calculate t. (Round your answer to 3 decimal places.)

(c-2) We reject the null hypothesis.

(d-1) Find the 95% confidence interval for slope. (Round your answers to 4 decimal places.)

(d-2) The confidence interval does not contain zero, which implies

(e) Calculate t2 and F. (Round your answers to 2 decimal places.)

1. Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable).
2. Answer the following questions.

(a) Using Data Set C, fill in the missing data. (Round your p-values to 4 decimal places and other answers to 2 decimal places.)

(b) The predictors whose p-values are less than 0.05 are (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)

(c) The predictors that were found to have significant coefficients from the t tests are the same ones that are significant from using the p-values.

(d) When checking for significance, most prefer the p-value approach because

5)         Consider the following Excel regression of perceived sound quality as a function of price for 27 stereo speakers.

(a) Is the coefficient of Price significantly different from zero at α = .05?

(b) Does R2 have any meaning?

(c) Given these results, would you conclude that a higher price implies higher sound quality?

6)         A researcher used stepwise regression to create regression models to predict CarTheft (thefts per 1,000) using four predictors: Income(per capita income), Unem (unemployment percent), Pupil/Tea(pupil-to-teacher ratio), and Divorce (divorces per 1,000 population) for the 50 U.S. states.

(a) Which model (Nvar 1, 2, 3, or 4) best balances fit and parsimony?

(b) Does the addition of Divorce improve the model with respect to the R2adj?

(c) Which two variables appear to be the most significant?

7)         Use the standard error to construct an approximate prediction interval for Y using an alpha of 5%. (Round your answer to 3 decimal places.)

8)         A hospital emergency room analyzed n = 17,664 hourly observations on its average occupancy rates using six binary predictors representing days of the week and two binary predictors representing the 8-hour work shift (12 a.m.–8 a.m., 8 a.m.-4 p.m., 4 p.m.–12 a.m.) when the ER census was taken. The fitted regression equation was AvgOccupancy = 11.2 + 1.19 Mon – 0.187 Tue – 0.785 Wed – 0.580 Thu – 0.451 Fri – 0.267 Sat – 4.58 Shift1 – 1.65 Shift2 (SE = 6.18, R2 = .094, R2adj = .093).

(a) Why did the analyst use only six binaries for days when there are 7 days in a week?

(b) The analyst used only two work shift binaries when there are three work shifts

(c) Which is the busiest day?

(d) Which is the busiest shift?

(e) The intercept represents the AvgOccupancy on Sundays during Shift 3.

9)         Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics.

10)       Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

11)       Consider the following data on 20 chemical reactions, with Y = chromatographic retention time (seconds) and X = molecular weight (gm/mole).

12)       Study the data sets (E, F, G, H, I) given below.

13)       In a model of Ford's quarterly revenue TotalRevenue = β0 + β1 CarSales + β2 TruckSales + β3 SUVSales + ε. The three predictors are measured in number of units sold (not dollars).

(a) Each slope measures the additional revenue earned by selling one more unit (one more car, truck, or SUV, respectively).

(b-2) Ford has to sell at least one car, truck, or SUV to earn revenue.

14)       Refer to the ANOVA table for this regression.

(a) State the degrees of freedom for the F test for overall significance.

(b) Use Appendix F to look up the critical value of F for α = .05. (Round your answer to 2 decimal places.)

(c-1) Calculate the F statistic. (Round your answer to 3 decimal places.)

(c-2) The overall regression is significant.

(c-3) The hypotheses are

15)       A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage.

(a) Fill in the values in the table given here for a two-tailed test at α = 0.01 with 39 d.f. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.)

(b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01 with 39 d.f? (Round your answer to 3 decimal places.)

(b-2) Choose the correct option.

16)       Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics.

(a) Write the regression model, being careful to exclude the base indicator variable. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

(b) Find the p-value for each coefficient, using 307 degrees of freedom. Using an α = .10, which predictor variable(s) are not significant predictors? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)

(c) By how much does the natural log of refrigerator price decrease from a two-door, side freezer model to a two-door, top freezer model? (Round your answer to 4 decimal places.)

(d) Which model demands a higher price: the side freezer or the one door with freezer model?

17)       Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

(a) Calculate the t statistic for each slope, at significance level = 0.01. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

18)       Refer to the ANOVA table for this regression.

(a) State the degrees of freedom for the F test for overall significance.

(b) Use Appendix F to look up the critical value of F for α = .05. (Round your answer to 2 decimal places.)

(c-1) Calculate the F statistic. (Round your answer to 3 decimal places.)

(c-2) The overall regression is significant.

(c-3) The hypotheses are

19)       Observations are taken on sales of a certain mountain bike in 22 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit).

(a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.)

(b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01? (Round your answer to 3 decimal places.)

(b-2) Choose the correct option.

20)       An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 22 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.07 bushels.

(a) Find the approximate width of a 95% prediction interval for wheat yield. (Round your answer to 2 decimal places.)

(b) Find the approximate width using the quick rule. (Round your answer to 2 decimal places.)

(c) The quick rule gives a similar result.

21)       Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable).

22)       Researchers found a correlation coefficient of r = .50 on personality measures for identical twins. A reporter interpreted this to mean that "the environment orchestrated one-half of their personality differences."

(a) r is a measure of the strength and direction of the linear relationship.

(b) r is a measure of the amount of variation.

23)       A regression model to predict Y, the state-by-state 2005 burglary crime rate per 100,000 people, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies per 1,000 people, X3 = 2004 federal expenditures per capita, and X4 = 2005 high school graduation percentage.

24)       Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

(a) Calculate the t statistic for each slope. From the p-values, which slopes differ from zero at α = .01? (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

(b) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.

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