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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

Question 124

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The model y = β0 + β1X1 + β2X2 + ε was fitted to a sample of 25 families in order to explain household milk consumption: where y = Milk consumption,in quarts,per week,x1 = Weekly income,in hundreds of dollars,and x2 = Family size.The least squares estimates of the regression parameters were b0 = -0.03,b1 = 0.05,and b2 = 1.1,with coefficient standard errors THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The model y = β<sub>0</sub> + β<sub>1</sub>X<sub>1</sub> + β<sub>2</sub>X<sub>2</sub> + ε was fitted to a sample of 25 families in order to explain household milk consumption: where y = Milk consumption,in quarts,per week,x<sub>1</sub> = Weekly income,in hundreds of dollars,and x<sub>2</sub><sub> </sub>= Family size.The least squares estimates of the regression parameters were b<sub>0</sub> = -0.03,b<sub>1</sub> = 0.05,and b<sub>2</sub> = 1.1,with coefficient standard errors = 0.02; = 0.38.The total sum of squares and the error sum of squares were found to be 165.8 and 66.32 respectively. -Test the hypothesis H<sub>0</sub> : β<sub>1</sub> = β<sub>2</sub> = 0<sub> </sub>against H<sub>1 </sub>:<sub> </sub>At least one β<sub>j</sub> ≠ 0,(j = 1,2)at the 1% significance level.
= 0.02; THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The model y = β<sub>0</sub> + β<sub>1</sub>X<sub>1</sub> + β<sub>2</sub>X<sub>2</sub> + ε was fitted to a sample of 25 families in order to explain household milk consumption: where y = Milk consumption,in quarts,per week,x<sub>1</sub> = Weekly income,in hundreds of dollars,and x<sub>2</sub><sub> </sub>= Family size.The least squares estimates of the regression parameters were b<sub>0</sub> = -0.03,b<sub>1</sub> = 0.05,and b<sub>2</sub> = 1.1,with coefficient standard errors = 0.02; = 0.38.The total sum of squares and the error sum of squares were found to be 165.8 and 66.32 respectively. -Test the hypothesis H<sub>0</sub> : β<sub>1</sub> = β<sub>2</sub> = 0<sub> </sub>against H<sub>1 </sub>:<sub> </sub>At least one β<sub>j</sub> ≠ 0,(j = 1,2)at the 1% significance level.
= 0.38.The total sum of squares and the error sum of squares were found to be 165.8 and 66.32 respectively.
-Test the hypothesis H0 : β1 = β2 = 0 against H1 : At least one βj ≠ 0,(j = 1,2)at the 1% significance level.

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Reject H0 if F > FK,n-K-1,α = F2,22,0.01 = 5.72
Since F = 16....

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