5 Test whether the coefficient associated with GAR is statistically different

5 test whether the coefficient associated with gar is

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4.5. Test whether the coefficient associated with GAR is statistically different from zero. Explain your workings. (2) 4.6. Explain the significance of the F statistic (249) displayed in the estimation results. (1) 4.7. Use the estimation results and construct the Analysis of Variance table. Explain your workings. (8) 4.8. Discuss whether the current model adequately captures the linear relationship between the response variable and the explanatory variables. (3) 4.9. Observations 20, 30, 46, 58 and 69 have high leverage values. Explain what this means. What is the cut off value for the leverage of an observation? (2) [ 28 ] 2
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Estimate Std. Error t value Pr(>|t|) (Intercept) 12.0509803 0.0569643 211.553 < 2e-16 *** YEARS.2 0.4457628 0.0481767 9.253 < 2e-16 *** YEARS.3 1.2391986 0.0473973 26.145 < 2e-16 *** AREA 0.0013173 0.0001584 8.318 3.24e-16 *** GAR 0.1972739 0.0179203 ??? ??? ??? BATH 0.1629377 0.0172384 9.452 < 2e-16 *** APART.1 -0.2037274 0.0450078 -4.526 6.79e-06 *** VIEW.1 0.2002969 0.0498911 4.015 6.44e-05 *** IMP.1 -0.1553814 0.0372520 -4.171 3.32e-05 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.4367 on 909 degrees of freedom Multiple R-Squared: 0.6867, Adjusted R-squared: 0.6839 F-statistic: 249 on ??? and ??? DF, p-value: < 2.2e-16 3
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SECTION B: Experimental Design PLEASE ANSWER IN A SEPARATE BOOK 5. The data below refers to a study aimed at determining the effect of different bleach concentrations (A=3, B=5 and C=7 teaspoonfuls per cup of water) and three types of stain (a=blue ink, b=jam and c=tomato sauce) on the time (seconds) taken to remove the stain from a piece of cloth. Five replications per treatment combination were used. (a) Referring to the first anova model in the output below (i) describe the design of the study (3) (ii) write down the anova model underlying this design, carefully explaining all terms in the model specification, and stating any constraints and assumptions underlying the model. (4) (b) Describe the decomposition of the bleach sums of squares that is represented and analysed in the second anova model, give reasons why such a decomposition is appropriate, and with the help of the graph, interpret the results presented in this part of the analysis. (5) (c) The graph seems to suggest that it may take longer to remove blue ink stains than stains from jam or tomato sauce. State the contrast that will formally test
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