1. In the production of a certain chemical it is believed the yield, Y, can be increased by increasing the amount of a particular catalytic agent. Twenty trials were made with different amounts of the catalyst. Analysis of the yields, measured in grams, and amounts of the catalyst, x, in milligrams gave: n = 20 22=2500 ^2=200 Lu=2780 y = = 387315 xy = 28150 (a) (10 points) Write the statistical model for a simple linear regres- sion of y on x and describe the assumptions for the error term. (b) (10 points) Using the given formulas, find the least squares re- gression line. (c) (10 points) Is there sufficient evidence the amounts of the catalyst is linearly and positively related to the yield? Answer by using a significance level a = .05. (d) (5 points) Construct 95% confidence interval for the slope. (e) (15 points) Predict the yield when the amounts of the catalyst is 15. Find a 95% confidence interval for the mean yield when the catalyst level is 15. Also, find a 95% prediction interval for a new observation when the catalyst level is 15. (f) (10 points) Calculate the coefficient of determination, and inter- pret the number you got.