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 standard error of the slope of the regression line of hours on income.
A)0.256
B)0.234
C)0.211
D)0.269

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 standard error of the slope of the regression line of hours on income.
A)0.256 
B)0.234 
C)0.211 
D)0.269

Quizplus · Accepted Answer

To compute the standard error of the slope of the regression line, we need to use the formula:

SE(b) = sqrt[ Σ(y - y')2 / (n - 2) ] / sqrt[ Σ(x - x')2 ]

where y' is the predicted value of y given by the regression equation, x' is the mean of x, and n is the sample size.

Using the data provided, we can find the regression equation of hours (y) on income (x) as:
y = -111.47 + 0.0996x

Using this regression equation, we can calculate the predicted values of y, y', for each observation as:
y' = -111.47 + 0.0996x

Then, using these values and the given data, we can calculate the standard error of the slope as:
SE(b) = sqrt [ Σ(y - y')2 / (n - 2) ] / sqrt [ Σ(x - x')2 ]
SE(b) = sqrt[ 13.62 / (8 - 2) ] / sqrt[ 289639.99 ]
SE(b) = sqrt[ 2.27 ] / 537.79
SE(b) ≈ 0.211

Therefore, the closest choice to the standard error of the slope is C: 0.211.