Solved: Interpreting a Computer Display. In Exercises 58, we want to consider the

Terminology Using the lengths (in.), chest sizes (in.), and weights (lb) of bears from Data Set 7 in Appendix B, we get this regression equation: Weight = 274 + 0.426 Length + 12.1 Chest Size . Identify the response and predictor variables.

Best Multiple Regression Equation For the regression equation given in Exercise 1, the Pvalue is 0.000 and the adjusted R 2 value is 0.925. If we were to include an additional predictor variable of neck size (in.), the Pvalue becomes 0.000 and the adjusted R 2 becomes 0.933. Given that the adjusted R 2 value of 0.933 is larger, is it better to use the regression equation with the three predictor variables of length, chest size, and neck size? Explain

Adjusted Coefficient of Determination For Exercise 2, why is it better to use values of adjusted R 2 instead of simply using values of R 2 ?

Interpreting R 2 For the multiple regression equation given in Exercise 1, we get R 2 = 0.928 . What does that value tell us?

Interpreting a Computer Display. In Exercises 58, we want to consider the correlation between LDL cholesterol and the predictor variables of weight (WT) and systolic blood pressure (SYS) for females. Refer to the Minitab display and answer the given questions or identify the indicated items. The Minitab display is based on the measured values of LDL cholesterol, weight, and systolic blood pressure amounts for the sample of 40 females from Data Set 1 of Appendix B. MINITAB LDL Cholesterol Identify the multiple regression equation that expresses the level of LDL cholesterol in terms of weight (WT) and diastolic blood pressure (SYS).

Interpreting a Computer Display. In Exercises 58, we want to consider the correlation between LDL cholesterol and the predictor variables of weight (WT) and systolic blood pressure (SYS) for females. Refer to the Minitab display and answer the given questions or identify the indicated items. The Minitab display is based on the measured values of LDL cholesterol, weight, and systolic blood pressure amounts for the sample of 40 females from Data Set 1 of Appendix B. MINITAB LDL Cholesterol Identify the following:LDL Cholesterol Identify the following: a. The Pvalue corresponding to the overall significance of the multiple regression equation b. The value of the multiple coefficient of determination R 2 c. The adjusted value of R 2

Interpreting a Computer Display. In Exercises 58, we want to consider the correlation between LDL cholesterol and the predictor variables of weight (WT) and systolic blood pressure (SYS) for females. Refer to the Minitab display and answer the given questions or identify the indicated items. The Minitab display is based on the measured values of LDL cholesterol, weight, and systolic blood pressure amounts for the sample of 40 females from Data Set 1 of Appendix B. MINITAB LDL Cholesterol Should the multiple regression equation be used for predicting the LDL cholesterol level based on weight and diastolic blood pressure? Why or why not?

Interpreting a Computer Display. In Exercises 58, we want to consider the correlation between LDL cholesterol and the predictor variables of weight (WT) and systolic blood pressure (SYS) for females. Refer to the Minitab display and answer the given questions or identify the indicated items. The Minitab display is based on the measured values of LDL cholesterol, weight, and systolic blood pressure amounts for the sample of 40 females from Data Set 1 of Appendix B. MINITAB LDL Cholesterol A female weighs 59.3 kg and she has a measured systolic blood pressure of 122 mm Hg. Use the multiple regression equation to determine the predicted LDL cholesterol amount. Is the result likely to be a good predicted value? Why or why not?

City Fuel Consumption: Finding the Best Multiple Regression Equation. In Exercises 912, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Predictor (x) Variables Pvalue R 2 Adjusted R 2 Regression Equation WT/DISP/HWY 0.000 0.943 0.933 CITY = 60.86 0.00128 WT 0.257 DISP + 0.652 HWY WT/DISP 0.000 0.748 0.720 CITY = 38.0 0.00395 WT 1.29 DISP WT/HWY 0.000 0.942 0.935 CITY = 6.69 0.00159 WT + 0.670 HWY DISP/HWY 0.000 0.935 0.928 CITY = 1.87 0.625 DISP + 0.706 HWY WT 0.000 0.712 0.697 CITY = 41.8 0.00607 WT DISP 0.000 0.659 0.641 CITY = 29.0 2.98 DISP HWY 0.000 0.924 0.920 CITY = 3.15 + 0.819 HWY If only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why?

City Fuel Consumption: Finding the Best Multiple Regression Equation. In Exercises 912, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Predictor (x) Variables Pvalue R 2 Adjusted R 2 Regression Equation WT/DISP/HWY 0.000 0.943 0.933 CITY = 60.86 0.00128 WT 0.257 DISP + 0.652 HWY WT/DISP 0.000 0.748 0.720 CITY = 38.0 0.00395 WT 1.29 DISP WT/HWY 0.000 0.942 0.935 CITY = 6.69 0.00159 WT + 0.670 HWY DISP/HWY 0.000 0.935 0.928 CITY = 1.87 0.625 DISP + 0.706 HWY WT 0.000 0.712 0.697 CITY = 41.8 0.00607 WT DISP 0.000 0.659 0.641 CITY = 29.0 2.98 DISP HWY 0.000 0.924 0.920 CITY = 3.15 + 0.819 HWY If exactly two predictor (x) variables are to be used to predict the city fuel consumption, which two variables should be chosen? Why?

City Fuel Consumption: Finding the Best Multiple Regression Equation. In Exercises 912, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Predictor (x) Variables Pvalue R 2 Adjusted R 2 Regression Equation WT/DISP/HWY 0.000 0.943 0.933 CITY = 60.86 0.00128 WT 0.257 DISP + 0.652 HWY WT/DISP 0.000 0.748 0.720 CITY = 38.0 0.00395 WT 1.29 DISP WT/HWY 0.000 0.942 0.935 CITY = 6.69 0.00159 WT + 0.670 HWY DISP/HWY 0.000 0.935 0.928 CITY = 1.87 0.625 DISP + 0.706 HWY WT 0.000 0.712 0.697 CITY = 41.8 0.00607 WT DISP 0.000 0.659 0.641 CITY = 29.0 2.98 DISP HWY 0.000 0.924 0.920 CITY = 3.15 + 0.819 HWYv Which regression equation is best for predicting city fuel consumption? Why?

City Fuel Consumption: Finding the Best Multiple Regression Equation. In Exercises 912, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Predictor (x) Variables Pvalue R 2 Adjusted R 2 Regression Equation WT/DISP/HWY 0.000 0.943 0.933 CITY = 60.86 0.00128 WT 0.257 DISP + 0.652 HWY WT/DISP 0.000 0.748 0.720 CITY = 38.0 0.00395 WT 1.29 DISP WT/HWY 0.000 0.942 0.935 CITY = 6.69 0.00159 WT + 0.670 HWY DISP/HWY 0.000 0.935 0.928 CITY = 1.87 0.625 DISP + 0.706 HWY WT 0.000 0.712 0.697 CITY = 41.8 0.00607 WT DISP 0.000 0.659 0.641 CITY = 29.0 2.98 DISP HWY 0.000 0.924 0.920 CITY = 3.15 + 0.819 HWYA Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?

Appendix B Data Sets. In Exercises 1316, refer to the indicated data set in Appendix B.Predicting Nicotine in Cigarettes Refer to Data Set 10 in Appendix B and use the tar, nicotine, and CO amounts for the cigarettes that are 100 mm long, filtered, nonmenthol, and nonlight (the last set of measurements). Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it best? Is the best regression equation a good regression equation for predicting the nicotine content? Why or why not?

Appendix B Data Sets. In Exercises 1316, refer to the indicated data set in Appendix B.. Predicting Nicotine in Cigarettes Repeat the preceding exercise using the sample data from the Menthol cigarettes listed in Data Set 10 from Appendix B.

Appendix B Data Sets. In Exercises 1316, refer to the indicated data set in Appendix B.Predicting IQ Score Refer to Data Set 6 in Appendix B and find the best regression equation with IQ score as the response (y) variable. Use predictor variables of brain volume and/or body weight. Why is this equation best? Based on these results, can we predict someone's IQ score if we know their brain volume and body weight? Based on these results, does it appear that people with larger brains have higher IQ scores?

Appendix B Data Sets. In Exercises 1316, refer to the indicated data set in Appendix B.Full IQ Score Refer to Data Set 5 in Appendix B and find the best regression equation with IQF (full IQ score) as the response (y) variable. Use predictor variables of IQV (verbal IQ score) and IQP (performance IQ score). Why is this equation best? Based on these results, can we predict someone's full IQ score if we know their verbal IQ score and their performance IQ score? Is such a prediction likely to be very accurate?

Testing Hypotheses About Regression Coefficients If the coefficient 1 has a nonzero value, then it is helpful in predicting the value of the response variable. If 1 = 0 , it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that 1 = 0 use the test statistic t = ( b 1 0 ) / s b 1 . Critical values or Pvalues can be found using the t distribution with n ( k + 1 ) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error s b 1 is often provided by software. For example, the Minitab display in Example 1 shows that s b 1 = 0.1289 (found in the column with the heading of SE Coeff and the row corresponding to the first predictor variable of the height of the mother). Use the sample data in Table 104 and the Minitab display in Example 1 to test the claim that 1 = 0 . Also test the claim that 2 = 0 . What do the results imply about the regression equation?

Confidence Interval for a Regression Coefficient A confidence interval for the regression coefficient 1 is expressed as b 1 E < 1 < b 1 + E where E = t / 2 s b 1 The critical t score is found using n ( k + 1 ) degrees of freedom, where k, n, and s b 1 are described in Exercise 17. Use the sample data in Table 104 and the Minitab display in Example 1 to construct 95% confidence interval estimates of 1 (the coefficient for the variable representing height of the mother) and 2 (the coefficient for the variable representing height of the father). Does either confidence interval include 0, suggesting that the variable be eliminated from the regression equation?

Dummy Variable Refer to Data Set 7 in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. (In Data Set 7, males are already represented by 1, but for females change the sex values from 2 to 0.) Letting the response (y) variable represent weight, use the variable of age and the dummy variable of sex to find the multiple regression equation. Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear? a. Female bear that is 20 years of age b. Male bear that is 20 years of age