Using the same data set, four models are estimated using the same response varia
ID: 3264407 • Letter: U
Question
Using the same data set, four models are estimated using the same response variable: however, the number of explanatory variables differs. Which model provides the best fit? a). Model 1 b). Model 2 c). Model 3 d). Model 4 In the estimation of a multiple regression model with two explanatory variables and 20 observations, SSE = 550 and SST = 1000. What is the value of R^2? a). 10 b). 45 c). 55 d). 90 Use the following scenario to answer questions (19) and (20): Over the past 30 years, the sample standard deviations of the annual rates of return for stock X and Stock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. In order to determine whether the correlation coefficient is significantly different from zero, the appropriate hypotheses are: a). H_o: mu = 0 and H_A: mu notequalto 0 b). H_o: p_xy = 0 and H_A: p_xy notequalto 0 c). H_o: mu = 1 and H_A: mu notequalto 1 d). H_o: p_xy = 1 and H_A: p_xy notequalto 1 When testing whether the correlation coefficient differs from zero, the value of the test statistic is t_test = 2.31. At the 5% significance level, the conclusion to the hypothesis test is to: a). Reject H_0: we can conclude that the correlation coefficient differs from zero. b). Reject H_0: we cannot conclude that the correlation coefficient differs from zero. c). Do not reject H_0: we can conclude that the correlation coefficient differs from zero. d). Do not reject H_0: we cannot conclude that the correlation coefficient differs from zero.Explanation / Answer
1. On the basis of the data given it can be seen that MODEL 1 is the better model when compared to the other models.We can say this because it has the higest value of adjusted r-square and the lowest standard error when the same number of observations are taken. We can also see that it has a high value of multiple R as well.
2.We know that SST = SSR +SSE
where SST- Total sum of squares and SSR- Sum of squares explained by the regression model and SSE- Error sum of squares
We are given SSE=550 and SST=1000
So, SSR=SST-SSE =1000-550=450
And, R2 =SSR/SST = 450/1000 =0.45
So, the correct answer is b) 0.45
3. The correct answer is b) H0: xy = 0 and HA:xy 0
Since, we have to test if the corelation coefficient is significantly different from zero we have to allow for both sides of deviatio thats is less than 0 and greater than 0 in ou alter native hypothesis.
4. Given, the value of the test statistic ttest =2.31
the number of observations 30. So the degrees of freedom we have 30-1 =29
The value of t-significant at 29 degrees of freedom is +/- 2.04522964.
Since, the value of our test statistic is greater than the significant value. So, we conclude that the test is significant. Hence, we reject the null hypothesis.
So, the correct answer is a) Reject H0 ; we can conclude that that the correlation coefficient differs from zero.
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