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Question 4. (25 points) A simple linear regression of the form y = ?? + ?? X? applied to 17 (x,y) data points resulting in the values ?? = 6.54 and ?? = 1.23 for the y-intercept and slope, respectively. The standard error of the regression line sigma hat (??) = 2.93, the variance of X = 2.60, and the variance of Y = 4.86. (Chapter 12) Note: Sxx = Var(X)(n-1) and S?? = Var(Y)(n-1) a) Given that the mean X = 2.8, what is the mean value of Y? b) What is the correlation r between X and Y? c) What is the R²-squared coefficient of determination for this regression line? d) Given that the t-statistic of the slope ?? equals 2.7 with 15 d.o.f., what is the F-statistic for this regression line? r = ??? ?(Sxx / S??) so that the sample correlation coefficient is simply a scaled version of the estimated slope parameter ???. Moreover, it turns out that r² = R² so that the square of the sample correlation coefficient is equal to the coefficient of determination of the regression model. This is because the F-statistic is the square of the t-statistic t² = F

          Question 4. (25 points)
A simple linear regression of the form y = ?? + ?? X? applied to 17 (x,y) data points resulting in the values ?? = 6.54 and ?? = 1.23 for the y-intercept and slope, respectively. The standard error of the regression line sigma hat (??) = 2.93, the variance of X = 2.60, and the variance of Y = 4.86. (Chapter 12) Note: Sxx = Var(X)*(n-1) and S?? = Var(Y)*(n-1)
a) Given that the mean X = 2.8, what is the mean value of Y?
b) What is the correlation r between X and Y?
c) What is the R²-squared coefficient of determination for this regression line?
d) Given that the t-statistic of the slope ?? equals 2.7 with 15 d.o.f., what is the F-statistic for this regression line?
r = ??? ?(Sxx / S??)
so that the sample correlation coefficient is simply a scaled version of the estimated slope parameter ???. Moreover, it turns out that
r² = R²
so that the square of the sample correlation coefficient is equal to the coefficient of determination of the regression model.
This is because the F-statistic is the square of the t-statistic
t² = F

Question 4. (25 points)
A simple linear regression of the form y = ?? + ?? X? applied to 17 (x,y) data points resulting in the values ?? = 6.54 and ?? = 1.23 for the y-intercept and slope, respectively. The standard error of the regression line sigma hat (??) = 2.93, the variance of X = 2.60, and the variance of Y = 4.86. (Chapter 12) Note: Sxx = Var(X)*(n-1) and S?? = Var(Y)*(n-1)
a) Given that the mean X = 2.8, what is the mean value of Y?
b) What is the correlation r between X and Y?
c) What is the R²-squared coefficient of determination for this regression line?
d) Given that the t-statistic of the slope ?? equals 2.7 with 15 d.o.f., what is the F-statistic for this regression line?
r = ??? ?(Sxx / S??)
so that the sample correlation coefficient is simply a scaled version of the estimated slope parameter ???. Moreover, it turns out that
r² = R²
so that the square of the sample correlation coefficient is equal to the coefficient of determination of the regression model.
This is because the F-statistic is the square of the t-statistic
t² = F

Added by Zachary W.

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