THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Consider a random sample of 25 observations of two variables x and y.The following summary statistics are available:
= 43.2,
= 195.6,
= 1357.2,
= 1253.4,and
= 4843.6.
-Determine the intercept of the regression line.
A)2.038
B)41.43
C)3.57
D)54.86

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Consider a random sample of 25 observations of two variables x and y.The following summary statistics are available:  
= 43.2,  
= 195.6,  
= 1357.2,  
= 1253.4,and  
= 4843.6.
-Determine the intercept of the regression line.
A)2.038 
B)41.43 
C)3.57 
D)54.86

Quizplus · Accepted Answer

The intercept of the regression line can be found using the formula: 
intercept = ȳ - slope * x̄ 
where ȳ and x̄ are the sample means of y and x, respectively, and slope is the sample regression coefficient.
From the information given, we know that:
x̄ = 43.2
ȳ = 195.6
slope = Σ[(xi - x̄)*(yi - ȳ)] / Σ(xi - x̄)^2 = 1,253.4 - 195.6*43.2 / 1,357.2 - 25*43.2^2 / (25-1) = 0.483
Substituting these values into the formula above, we get:
intercept = 195.6 - 0.483 * 43.2 = 41.43
Therefore, the best choice is B.