3. Jeff Hittinger is a founder and brewmaster of the Octonia Stone Brew Works in Ruckersville, Virginia. He is contemplating the purchase of a particular type of malt (that is, roasted barley) to use in making certain types of beer. Specifically, he wants to know whether there is a simple linear regression relationship between the mashing temperature (the temperature of the water in which the malted barley is cooked to extract sugar) and the amount of maltose sugar extracted. After conducting 12 trials, he obtains the following data, expressed in terms of (temperature in Fahrenheit, maltose sugar content as a percentage of the total sugar content in the liquid):
(155,25),(160,28),(165,30),(170,31),(175,31),(180,35),(185,33),(190,38),(195,40),
(200,42),(205,43),(210,45)
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(a) Calculate the least squares estimators of the slope, the y-intercept, and the variance based upon these data. (b) What is the coefficient of determination for these data? (c) Conduct an upper-sided model utility test for the slope parameter at the 5% significance level. Would you reject the null hypothesis at that significance level?