Refer to Brand preference data used in the previous exercise.1. Test, jointly, whether there is a linear relationship between Y and (X1, X2), using = 0.01.State the alternatives, decision rule, and conclusion. What does your test imply about 1 and2?2. Calculate the coefficient of multiple determination R2. How is it interpreted here?3. Calculate the adjusted R2. Does it equal the coefficient of multiple determination in part (2)?Justify your answer.4. Obtain an interval estimate of E(Yh) when Xh1 = 5 and Xh2 = 4. Use a 99% confidencecoefficient. Interpret your interval estimate.5. Obtain a prediction interval for a new observation Yh(new) when Xh1 = 5 and Xh2 = 4. Use a99% confidence coefficient.”Y” “X_1” “X_2”
“1” 64 4 2
“2” 73 4 4
“3” 61 4 2
“4” 76 4 4
“5” 72 6 2
“6” 80 6 4
“7” 71 6 2
“8” 83 6 4
“9” 83 8 2
“10” 89 8 4
“11” 86 8 2
“12” 93 8 4
“13” 88 10 2
“14” 95 10 4
“15” 94 10 2
“16” 100 10 4Refer to Brand preference data used in the previous exercise.1. Test, jointly, whether there is a linear relationship between Y and (X1, X2), using = 0.01.State the alternatives, decision rule, and conclusion. What does your test imply about 1 and2?2. Calculate the coefficient of multiple determination R2. How is it interpreted here?3. Calculate the adjusted R2. Does it equal the coefficient of multiple determination in part (2)?Justify your answer.4. Obtain an interval estimate of E(Yh) when Xh1 = 5 and Xh2 = 4. Use a 99% confidencecoefficient. Interpret your interval estimate.5. Obtain a prediction interval for a new observation Yh(new) when Xh1 = 5 and Xh2 = 4. Use a99% confidence coefficient.