The index of deflated turnover for retail trade shows the activity in volume of the retail trade sector. This index is reported with 2005: 100. The accompanying table holds the index for 43 countries for the years 2007 and 2010. Complete parts a) through d). a) Find a regression model predicting the 2010 index from the index in 2007 for the sample of 43 countries. Winds}: D + [I x 2007 index (Round to three decimal places as needed.) b) Examine the residuals to determine if a linear regression is appropriate. Construct a plot of the residuals against x. Choose the correct graph below. ij- A. i] B. i] C. 50 Q 50 Q . O 25 0 s ' O' s O' s .12 .12 .12 m r. i. Q ['1' Q ['1' 2 > 80 100 120 140 160 > 80 100 120 140 160 > 80 100 120 140 160 2007 Index 2007 Index 2007 Index Construct a Normal probability plot of the residuals. Choose the correct graph below. ij- A. i] B. i] C. Q 50 Q O\\ 2 2 m m m :3 :3 :3 a? a 5 5 Normal Scores Normal Scores Normal Scores Evaluate the plots to determine if a linear regression is appropriate. Choose the correct answer below. i.\" A. The plot of the residuals against x shows no pattern, which satises the conditions for linear regression. The Normal probability plot indicates that the Normal Probability Assumption is violated. -' . B. The plot of the residuals against x shows no pattern, which is a possible violation of the Independence Assumption. The Normal probability plot indicates that the Normal Probability Assumption is violated. -" V C. The plot of the residuals against x tends to spread out as x increases, which is a possible violation of the Equal Variance Assumption. The Normal probability plot indicates that the Normal Population Assumption is satised. D. The plot of the residuals against x tends to cluster as x increases, which is a possible violation of the Linearity Condition. The Normal probability plot indicates that the Normal Population Assumption is satised. c) Test an appropriate hypothesis using or: 0.05 to determine if the association is signicant. Choose the correct null and alternative hypotheses. If" A. H0431=0 HA: [)1 #0 '3' 5- H03 I30 = I31 HA: I30 * 51 O. H0: [30 =0 HA: [)0 #0 C.\" D. H0: I30 = [)1 =0 HA: po#0 or [31 #0 Determine the test statistic. t=|: (Round to two decimal places as needed.) Determine the Pvalue. P-value = :| (Round to three decimal places as needed.) Make a conclusion. Since the P-value is the significance level, a, the null hypothesis. The association significant. d) What percentage of the variability in the 2010 Index is accounted for by the regression model? The regression model accounts for % of the variability in the 2010 Index. (Round to one decimal palce as needed.)Country Index 2007 | Index 2010 109.9 116.8 102.3 106.4 W 134.8 170.5 4 103.6 104.2 5 134.3 125.2 6 111.6 119.4 90.7 135.1 116.6 124.1 9 115.1 118.6 10 116.7 118.2 11 102.9 94.3 12 130.9 101.2 13 109.6 111.7 14 106.7 112.5 15 98.9 97.1 16 110.6 93.4 17 103.1 93.5 18 115.8 78.3 19 115.4 106.4 20 101.2 96.8 21 99.6 100.9 22 109.3 120.8 23 138.4 91.4 24 121.8 92.3 25 108.4 122.9 26 104.1 104.3 27 104.8 104.6 28 107.8 101.3 29 107.9 103.2 30 112.5 116.4 31 124.3 143.6 32 101.4 99.1 33 111.8 143.7 34 143.9 147.7 35 132.6 151.8 36 113.7 109.4 37 109.2 108.9 38 119.6 121.2 39 104.8 91.6 40 107.1 111.1 41 107.5 114.9 42 107.7 112.4 43 102.5 94.7