Use the following data to answer the questions below:

Question

a. Find the regression coefficients (the intercept and slope coefficients).

b. Estimate the standard error of the residuals about the regression line.

c. Find the value of R2.

Answer 1

a. First, we find xmean and ymean, which are 823.00 and 26.75 respectively. Taking the sum of the products of the difference of each record with its respective mean, we find sigma{i=1 to n} (xi
-xmean)(yi-ymean) = (867 - 823)(12 - 26.75) + ... = 22606
while the sum of the squares differences between the x values and xmean is
sigma{i=1 to n} (xi - xmean)
2= (867 - 823)2... = 480280
Thus
b = 22606 / 280280 = 0.047
a = ymean - b * xmean = 26.750 - 0.047 * 823.000 = -11.931

b. The standard error is given by the square root of the sum of squared differences between actual and predicted y values divided by n - 2. Thus, we know that:
sigma{i=1 to n} (yi - ymean) 2 = (12 - 26.75)2 ... = 6423.75.
So that the standard error is
Standard error = sqrt( 6423.75 / (20 - 2)) = 18.891

c. R2
can be found by calculating the correlation coefficient from the slope and the standard
deviations of the samples and then squaring it. We find that sx and sy

are 158.990 and

18.387, respectively. Thus, drawing on part (a) we find that
r = b * sx / sy

= 0.047 * 158.990 / 18.387 = 0.406

r
2
= 0.4062
= 0.165