Question 3 regression model with Y as response variable and X as the explanatory

Question

Question 3 regression model with Y as response variable and X as the explanatory variable. We drew the two-way scatter plot for X and Y. Also, we obtain the following SAS output Using a data with n = 200 observations, we fit a simple linear scatter plot -1 A few items have been removed from the SAS output and replaced by clusters of x's. Analysis of Variance F-Value Prob F Source Model Error Total DF Sum of Squares 437.82 Mean Square 437.82 1.19 Oxx 199 673.92 What is the value of the F statistic in this analysis? What are the degrees of freedom for numerator and denominator of this F statistic? What are the null hypothesis and alternative hypothesis for this overall F test showing the above table? What can you conclude based on the testing results? What is the proportion of the variability among observed values of Y that is explained by the linear regression model of Y on X? (a) 35% (b) 65% (c) 42% (d) 81% (e) 59% What is Pearson correlation coefficient between X and Y? (a) 0.59 (b) 0.81 (c)-0.59 (d)-0.81 (e) 0.65

Explanation / Answer

Here dF (error) = n -2 = 200 - 2= 198

SS(error) = MSE * dF = 1.19 * 198 = 235.62

Question 1

R2 = SSR/SST = 437.82/ 673.92 = 64.96% or say 65% so Option B is correcct.

(2) Pearson Correlation Coefficient

r = sqrt(R2) = +- sqrt (0.6496) =  +- 0.8060 or

here the linear relationship is negative so we will take negative value

r = - 0.81

Option D is correct here.

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