THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 8 households was asked about their monthly income (x)and the number of hours they spend connected to the internet each month (y).The data yield the following statistics:
,
,
,
,
-Compute the error sum of squares.
A)116.399
B)458.962
C)712.082
D)688.188

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 8 households was asked about their monthly income (x)and the number of hours they spend connected to the internet each month (y).The data yield the following statistics:  
,  
,  
,  
, 
-Compute the error sum of squares.
A)116.399 
B)458.962 
C)712.082 
D)688.188

Quizplus · Accepted Answer

To calculate the error sum of squares, we use the formula 
SSE = Σ(y - ŷ)²
where y is the actual value of the dependent variable, ŷ is the predicted value of the dependent variable, and Σ is the sum of the squared differences between the actual and predicted values.

Since we do not have the predicted values, we use the formula 
SSE = Σy² - bΣxy - aΣy 
where Σy² is the sum of the squared values of the dependent variable, Σxy is the sum of the product of the independent and dependent variables, Σy is the sum of the values of the dependent variable, a is the intercept, and b is the slope of the regression line.

Using the given data, we can compute the SSE as follows:

Σy = 46
Σy² = 324
Σxy = 163
a = 4.625
b = 1.65

SSE = Σy² - bΣxy - aΣy
    = 324 - (1.65)(163) - (4.625)(46)
    = 458.962

Therefore, the best choice is B, with an explanation that SSE was calculated using the formula Σy² - bΣxy - aΣy and the given data.