Consider the regression fit denoted as \"Model A\". a) What are the estimates of

Question

Consider the regression fit denoted as "Model A". a) What are the estimates of beta_0, beta_1, beta_2, and beta_3 for this regression? b) What is the estimate of mu_y|x_1, x_2 for this regression? Note that the answer will be in terms of x_1 and x_2. c) What is the estimate of sigma^2 for this regression? d) Report the t distributed 95% confidence interval for beta_2. (No calculation necessary) e) Describe what the p-values for the beta parameters tell us. f) Report the t distributed 95% confidence interval for the mean price sold for a machine with 18 replaced parts and satisfaction index of 68.5. Also, give the interpretation of this interval. (No calculation necessary)

Explanation / Answer

Part-a

WE have 0=9258.647   2=-251.2051       2=2.1562131     3=-0.489372

Part-b

We have µy|x1,x2 =9258.647-251.2051 x1 -0.489372 x2

Part-c

Estimate of 2 is =MSE=600187.42

Part-d

95% confidence interval for 2= (1.7800987 , 2.5323275)

Part-e

p-value of parameters tells us whether the coefficient is significant and so predictor help in predicting response variable

If p<0.05, we conclude the predictor is significant other wise not

Part-f

Predicted mean price= 9258.647 -251.2051*18+2.1562131*18*18-0.489372*68.5=5402.046262

95% confidence interval tells us that the interval contains the true mea price for all machine with 18 replaced parts and satisfaction index of 68.5.

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