Refer to the sleep deprivation experiment described in Exercises 12.11 and 12.12 and data set EX1211. The data and the MINITAB and MS Excel printout are reproduced here.

MINITAB output for Exercise 12.26
Regression Analysis: y versus x
The regression equation is
y = 3.00 + 0.475 x

MS Excel output for Exercise 12.26

a. Do the data present sufficient evidence to indicate that the number of errors is linearly related to the number of hours without sleep? Identify the two test statistics in the printout that can be used to answer this question.
b. Would you expect the relationship between y and x to be linear if x varied over a wider range (say, x = 4 to x = 48)?
c. How do you describe the strength of the relationship between y and x?
d. What is the best estimate of the common population variance s2?
e. Find a 95% confidence interval for the slope of the line.

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Number of Errors, y Number of Hours without Sleep, x 812 16 Number of Errors, y Number of Hours without Sleep, x 20 24 8, 6 6, 10 8, 14 14, 12 16, 12 Predictor Constant Coef SE Coef 3.000 2.127 1.4 0.196 0.4750 0.1253 3.79 0.005 S= 2.24165 R-Sq 64.2% R-Sq (adj) 59.8s = = Analysis of Variance Source Regression Residual Error 840.200 .025 Total DF MS 1 72.200 72.200 14.37 0.005 9 112.400 ANOVA df MS F Significance F 0.005 Regression Residual Total 172.2 8 40.2 5.025 9 112.4 72.2 14.368 Coefficients Standard Error р. value Lower Upper 95% Stat 95% Intercept 3 2.1266 1.4107 0.1960 1.9040 7.9040 0.1860 0.7640 0.475 0.1253 3.7905 0.0053