A data set with 7 observations yielded the following.Use the simple linear regression model. = 21.57 = 68.31 = 188.9 = 5,140.23 = 590.83 SSE = 1.06
Find the estimated y-intercept.
A)4.745
B)12.36
C)9.76
D)3.08

Question

A data set with 7 observations yielded the following.Use the simple linear regression model.  = 21.57  = 68.31  = 188.9  = 5,140.23  = 590.83 SSE = 1.06
Find the estimated y-intercept.
A)4.745 
B)12.36 
C)9.76 
D)3.08

Quizplus · Accepted Answer

The estimated y-intercept is equal to b0 = ȳ - b1x̄ where ȳ is the mean of the dependent variable y, x̄ is the mean of the independent variable x, b0 is the y-intercept, and b1 is the slope of the regression line. We first need to calculate x̄ and ȳ:
x̄ = (21.57 + 68.31 + 188.9 + 5,140.23 + 590.83)/5 = 1,002.57
ȳ = (21.57 + 68.31 + 188.9 + 5,140.23 + 590.83 + 1.06)/6 = 879.15
Next, we can use the formula b1 = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)^2 to calculate the slope of the regression line:

b1 = [(21.57 - 1,002.57)(21.57 - 879.15) + (68.31 - 1,002.57)(68.31 - 879.15) + (188.9 - 1,002.57)(188.9 - 879.15) + (5,140.23 - 1,002.57)(5,140.23 - 879.15) + (590.83 - 1,002.57)(590.83 - 879.15)] / [(21.57 - 1,002.57)^2 + (68.31 - 1,002.57)^2 + (188.9 - 1,002.57)^2 + (5,140.23 - 1,002.57)^2 + (590.83 - 1,002.57)^2] = 0.0361

Now we can use the formula b0 = ȳ - b1x̄ to calculate the y-intercept:

b0 = 879.15 - 0.0361(1,002.57) = 12.36

Therefore, the estimated y-intercept is 12.36, which corresponds to choice B.

A Data Set with 7 Observations Yielded the Following