Question

Researchers were interested in the relationship between the number of hours per week on Facebook and perceived loneliness (higher the score, the lonelier the individual) in older adults. Using the tables below, answer the following questions.

1. Is there a significant relationship time spent on Facebook and perceived loneliness? Explain your answer.

2. Write out the regression equation.

3. Given the calculated regression equation (see question 6), calculate Y' for each of the following values of X:

10

                            

15

                            

25

Regression

ANOVAa
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	33.822	1	33.822	45.941	.000b
	Residual	182.578	248	.736
	Total	216.400	249

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	.708	.126		5.605	.000
	Facebook	.027	.004	.395	6.778	.000

Answer 1

Is there a significant relationship time spent on Facebook and perceived loneliness? Explain your answer.

Yes there is a significant relationship time spent on Facebook and perceived loneliness.

Explanation :

The p-value for estimating the slope corresponding to the Facebook is = 0.000 (Sig. value in the last column and last row of the Coefficientsa table).

Here p-value is approximately equal to zero so we conclude that the slope is significant.

This implies that there is a significant relationship time spent on Facebook and perceived loneliness.

Write out the regression equation.

let x = time spent on Facebook,  

y = perceived loneliness

The general formula of estimated regression equation is as

From the Coefficientsa table , we have

This is the regression equation.

Given the calculated regression equation (see question 6), calculate Y' for each of the following values of X:

Let's plug x values in the regression equation, we get:

For X = 10, we have

For X = 15, we have

For X = 25, we have