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(d) Fill in the blanks in the following table. Source of Variation DF Mean Square F Value Sum of Squares SSR = 16059 1 MSR = 16058.9 ? Regression Residual 12 ? = ? SSE = ? MSE=15366 ? (e) (i) Write down the null hypothesis, that there is no effect on mean sales from increasing the amount of shelf space, versus a suitable alternative hypothesis. (ii) Compare the above value of F with the table value F(0.01). (iii) Comment on your findings.

(d) Fill in the blanks in the following table. Source of Variation DF Mean Square F Value Sum of Squares SSR = 16059 1 MSR = 16058.9 ? Regression Residual 12 ? = ? SSE = ? MSE=15366 ? (e) (i) Write down the null hypothesis, that there is no effect on mean sales from increasing the amount of shelf space, versus a suitable alternative hypothesis. (ii) Compare the above value of F with the table value F(0.01). (iii) Comment on your findings.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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(d) Fill in the blanks in the following table. Source of Variation DF Mean Square F Value Sum of Squares SSR = 16059 1 MSR = 16058.9 ? Regression Residual 15366 12 ?? SSE = ? MSE = = ? (e) (i) Write down the null hypothesis, that there is no effect on mean sales from increasing the amount of shelf space, versus a suitable alternative hypothesis. (ii) Compare the above value of F with the table value Fl(0.01). (iii) Comment on your findings.
Transcribed Image Text:(d) Fill in the blanks in the following table. Source of Variation DF Mean Square F Value Sum of Squares SSR = 16059 1 MSR = 16058.9 ? Regression Residual 15366 12 ?? SSE = ? MSE = = ? (e) (i) Write down the null hypothesis, that there is no effect on mean sales from increasing the amount of shelf space, versus a suitable alternative hypothesis. (ii) Compare the above value of F with the table value Fl(0.01). (iii) Comment on your findings.
A baker is interested to find the relationship between the width of the shelf space for her brand of cookies (x, in feet) and monthly sales (y) of the product in a supermarket. Hence, she fits a model relating monthly sales y to the amount of shelf space x her cookies receive that month. That is, she is fitting the model in the following way y=B+₂x+e where ~ N(0,0¹). x (shelf space) y (weekly sales) weekly sales VS shelf space 3 2 6 575 5 3 450 8 630 4 435 2 498 6 534 3 530 2 457 7 2 3 5 7 Using R, we obtained the following output. > mody <- 1m (y - x) > summary (mody) Call: lm (formula y - x) Residuals: Min 10 Median 3Q Max -67.022 -31.346 -0.631 33.654 54.734 Coefficients: (Intercept) 429.048 26.519 16.179 1.69e-08 *** x 18.244 5.643 3.233 0.00898 ** Signif. codes: 0*** 0.001 **0.01 0.05 0.11 Residual standard error: 39.2 on 10 degrees of freedom Multiple R-squared: 0.511, Adjusted R-squared: 0.4621 F-statistic: 10.45 on 1 and 10 DF, p-value: 0.008979 > anova (mody) Analysis of Variance Table Response: y X 1 Df Sum Sq Mean Sq F value Pr (>F) 16059 16058.9 10.451 0.008979 ** Residuals 10 15366 1536.6 Signif. codes: 0 '*** 0.001 '**' 0.01 0.05. 0.11 8 4 Estimate Std. Error t value Pr(>|t|) .
Transcribed Image Text:A baker is interested to find the relationship between the width of the shelf space for her brand of cookies (x, in feet) and monthly sales (y) of the product in a supermarket. Hence, she fits a model relating monthly sales y to the amount of shelf space x her cookies receive that month. That is, she is fitting the model in the following way y=B+₂x+e where ~ N(0,0¹). x (shelf space) y (weekly sales) weekly sales VS shelf space 3 2 6 575 5 3 450 8 630 4 435 2 498 6 534 3 530 2 457 7 2 3 5 7 Using R, we obtained the following output. > mody <- 1m (y - x) > summary (mody) Call: lm (formula y - x) Residuals: Min 10 Median 3Q Max -67.022 -31.346 -0.631 33.654 54.734 Coefficients: (Intercept) 429.048 26.519 16.179 1.69e-08 *** x 18.244 5.643 3.233 0.00898 ** Signif. codes: 0*** 0.001 **0.01 0.05 0.11 Residual standard error: 39.2 on 10 degrees of freedom Multiple R-squared: 0.511, Adjusted R-squared: 0.4621 F-statistic: 10.45 on 1 and 10 DF, p-value: 0.008979 > anova (mody) Analysis of Variance Table Response: y X 1 Df Sum Sq Mean Sq F value Pr (>F) 16059 16058.9 10.451 0.008979 ** Residuals 10 15366 1536.6 Signif. codes: 0 '*** 0.001 '**' 0.01 0.05. 0.11 8 4 Estimate Std. Error t value Pr(>|t|) .
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