The second slide is the first part of the question and the first slide is the second part of the question. (e)Use the F test to test the hypotheses in part (d) at a 0.05 level oF significance. Present the results in the analysis of variance table format.Set up the ANOVA table. (Round your values for MSE and Fto two decimal places, and your p-value to three decimal places.)Sourceof VariationSureof SquaresHeanN FreedonnpvalueRegressionErrorTotalFind the value of the test statistic. (Round your answer to two decimal places.)tFind the p-value. (Round your answer to three decimal places.)p-valueState your conclusion.O Do not reject H. We conclude that the relationship between x and y is significant.O Reject H,. We conclude that the relationship between x and y is significant.O Do not reject H,. We cannot conclude that the relationship between x and y is significant.O Reject H,. We cannot conclude that the relationship between x and y is significant. Consider the data.1.2.42 8113SSE(a) Compute the mean square error using equation s = MSE(Round your answer to two decimal places.)2SSE(b) Compute the standard error of the estimate using equation s = V MSE =(Round your answer to three decimal places.)n- 2(c) Compute the estimated standard deviation of b, using equation s, = =ZV>(x, - x)*(Round your answer to three decimal places.)(d) Use the t test to test the following hypotheses (a = 0.05):Hg: B, = 0H. B, 0Find the value of the test statistic. (Round your answer to three decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.O Do not reject H. We conclude that the relationship between x and y is significant.O Reject H.. We conclude that the relationship between x and y is significant.O Do not reject H,. We cannot concl ude that the relationship between xand y is significant.O Reject H,. We cannot conclude that the relationship betweenx and y is significant.

Name: The second slide is the first part of the question and the first slid
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: The second slide is the first part of the question and the first slide is the second part of the question. (e)Use the F test to test the hypotheses in part (d) at a 0.05 level oF significance. Present the results in the analysis of variance table fo

Note: According to the guidelines, only first three subparts have been solved. Given information: x 1 2 3 4 5 y 2 8 6 11 13a) The required calculations are shown in this table : x 1 2 3 4 5 ∑x=15 y 2 8 6 11 13 ∑y=40 xy 2 16 18 44 65 ∑xy=145 x2 1 4 9 16 25 ∑x2=55 Firstly, calculation of regression line is necessary for MSE: y^=a+bx^ where, y^=dependent variablex^=independent variable a = y intercept. b = slope of the regression line. Now, b=n∑xy-∑x∑yn∑x2-∑x2=5(145)-15405(55)-152=2.5 a=y¯-bx¯=405-2.5155=0.5 Therefore, y^=0.5+2.5 x^ Hence, for the different value of x, y^ 3 5.5 8 10.5 13 ∑y=40 (y-y^)2 1 6.25 4 0.25 0 ∑y-y^2=11.5 Calculation of mean square error is: s2=SSEn-2=∑(y-y^)25-2=11.53=3.83 Therefore, the value of mean square error is 3.83. b) Calculation of standard error: s=SSEn-2=∑(y-y^)25-2=11.53=1.958 Therefore, the value of standard error is 1.958.c) Calculation of estimated standard deviation of b1: Mean of x is computed as: x¯=∑xn=155=3 x 1 2 3 4 5 ∑x=15 (x-x¯)2 4 1 0 1 4 ∑(x-x¯)2=10 sb1=s∑(x-x¯)2=1.95810=0.619 Therefore, the value of estimated standard deviation is 0.619.