The following Minitab output describes the results of a production experiment in which n = 10 different steel bars were subjected to tempering times ranging from 6 to 10 seconds, then measured for tensile strength (thousands of pounds):

a. To the greatest number of decimal places in the printout, what is the least-squares regression line?
b. What proportion of the variation in strength is explained by the regression line?
c. At what level of significance does the slope of the line differ from zero? What type of test did Minitab use in reaching this conclusion?
d. At what level of significance does the coefficient of correlation differ from zero? Compare this with the level found in part (c) and explain either why they are different or why they are the same.
e. Construct the 95% confidence interval for the slope of the population regression line.

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Regression Analysis The regression equation is STRENGTH 60.0 10.5 TEMPTINE Predictor Constant TEMPTIME Coef 60.02 10.507 StDev 29.36 3.496 2.04 0.075 3.01 0.017 14.03 R-Sq 53.0% R-Sq(adj) 47.2% - : Analysis of Variance Source Regression Error Total DF 1 sS MS 9.03 0.017 1574.6 3352.0 196.8