SE(Cooff) t-ratio The output to the right shows the regression of the 2006 cost
ID: 2927531 • Letter: S
Question
SE(Cooff) t-ratio The output to the right shows the regression of the 2006 cost of living index on the 2007 index for the most expensive cities in the world. The 2007 index is the Predictor response variable. Complete parts a through d below. Coeff 2.73 1.573 P-value 0.3800 0.0001 14.10 Intercept Index 2006 s= 4.87 0.90 6.12 0.257 R-Sq = 85.5% a) State the hypotheses about the slope Ho: There is | no | linear relationship between the index in 2006 and 2007 (A HA: There is | | linear relationship between the index in 2006 and 2007 (A b) Perform the hypothesis test and state your conclusion in context The test statistic is ). The P-value is State your conclusion. Choose the correct answer below. O A. Reject the null hypothesis. There is insufficient evidence of a linear relationship between the two indices. O B. Fail to reject the null hypothesis. There is sufficient evidence of a linear relationship between the two indices. O C. Reject the null hypothesis. There is sufficient evidence of a linear relationship between the two indices. O D. Fail to reject the null hypothesis. There is insufficient evidence of a linear relationship between the two indices. c) Explain what the R-squared in this regression means. A. ( B. ° C. O D. The percentage of the variation in the 2006 index accounted for by the 2007 index is 85.5%. Overall, the 2007 index is 14.5% of the 2006 index. The percentage of the variation in the 2007 index accounted for by the 2006 index is 85.5%. Overall, the 2006 index is 85.5% of the 2007 index.Explanation / Answer
Answer to the question is as follows:
a.
Ho: 'no', B1 = 0
Ha: 'a' , B1 !=0
Test statistic= (Coefficient of Index 2006)/SE = 1.573/.257 = 6.12.
The p-value is <0.0001
b. C is right. So, we reject the null hypothesis. There is sufficient eveidence of a linear relationship between the 2 indices
c. C is right. That is the right interpretation of Rsquare. and the dependent variable is index of 2007
d. B is right. Yes, because there is sufficient evidence of a linear lreationship with a positive slope. The slope is at 1.573
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