STAT-UB.0103.04-Statistics for Business Control and Regression Models December 9, 2015 Homework 8-due December 15 Reading: From MBS: 12.1-12.4, 12.6 (up to page 700), 12.7, 12.11-12.12 Lecture Notes #22 1) A survey of a random sample of 47 NYU undergraduate students was conducted to investigate the relationship between Sleep=average sleep time per night (in hours) and the following variables: Study =average study time per day (in hours) CupsCoee =average number of cups of coee consumed by a student per day, and Age (in years) Answer questions below based on the Minitab output on the next two pages. a) Is the estimated multiple linear regression model of Sleep on the variables listed above statistically signicant at = 0 01? (State the relevant hypothesis test and your conclusion) b) Compute 2 of the multiple linear regression model and interpret it. c) Which two explanatory variables are most highly correlated with each other? Which two explanatory variables exhibit the smallest correlation? d) Identify predictor(s) that are statistically signicant at = 0 05 in the simple regressions but are not statistically signicant at = 0 05 in the multiple regression. Give a reason for their lack of statistical signicance in the multiple regression. e) The two-variable model with CupsCoee and Study was chosen as the nal model. Interpret the coecients in this model. f ) Before tting the multiple regression models the students hypothesized that for every one cup increase in CupsCoee, the expected decrease in Sleep is 0.4 of an hour. Based on the nal model were they correct? Answer by constructing an appropriate 95% condence interval. g) Construct a 95% condence interval for the average sleep time of students who study 4 hours and drink 6 cups of coee. Is this a valid condence interval? Explain. 1 Regression Analysis: Sleep versus Age, Study, Cupscoffee The regression equation is Sleep = 4.91 + 0.0449 Age + 0.231 Study - 0.357 Cupscoffee Predictor Constant Age Study Cupscoffee Coef 4.9100 0.04486 0.23083 -0.35740 SE Coef 0.8070 0.03955 0.07268 0.09061 T 6.08 1.13 3.18 -3.94 P 0.000 0.263 0.003 0.000 S = 0.852758 Analysis of Variance Source Regression Residual Error Total DF 3 43 46 SS 20.6029 31.2694 51.8723 MS 6.8676 0.7272 F 9.44 P 0.000 Correlations: Sleep, Age, Study, Cupscoffee Sleep 0.296 0.043 Cupscoffee 0.369 0.011 -0.410 0.004 Study Age 0.390 0.007 Age 0.001 0.997 Study 0.155 0.297 Regression Analysis: Sleep versus Study, Cupscoffee The regression equation is Sleep = 5.75 + 0.262 Study - 0.364 Cupscoffee Predictor Constant Study Cupscoffee Coef 5.7544 0.26166 -0.36377 S = 0.855534 SE Coef 0.3130 0.06763 0.09073 R-Sq = 37.9% T 18.39 3.87 -4.01 P 0.000 0.000 0.000 R-Sq(adj) = 35.1% Analysis of Variance Source Regression Residual Error Total DF 2 44 46 SS 19.6671 32.2053 51.8723 MS 9.8335 0.7319 F 13.43 P 0.000 Predicted Values for New Observations New Obs 1 Fit SE Fit 0.417 Values of Predictors for New Observations New Obs 1 Study 4.00 Cupscoffee 6.00 Descriptive Statistics: Sleep, Study, Cupscoffee Variable Sleep Study Cupscoffee N 47 47 47 N* 0 0 0 Variable Sleep Study Cupscoffee Maximum 9.000 10.000 8.000 Mean 6.213 4.000 1.617 SE Mean 0.155 0.275 0.205 StDev 1.062 1.888 1.407 Minimum 4.000 1.000 0.000 Q1 5.000 3.000 1.000 Median 6.000 4.000 1.000 Q3 7.000 5.000 2.000