Question

Critics of television often refer to the detrimental effects that all the violence shown on television has on children. However, there may be another problem. It may be that watching television also reduces the amount of physical exercise, causing weight gains. A sample of 15 10-year-old children was taken. The number of pounds each child was overweight was recorded (a negative number indicates the child is underweight). In addition, the number of hours of television viewing per week was also recorded. These data are listed here. (also provided in the Excel Spreadsheet) Television 42 34 25 35 37 38 31 33 Overweight 18 6 0 −1 13 14 7 7 Television 19 29 38 28 29 36 18 Overweight −9 8 8 5 3 14 −7 REQUIRED a) Draw the scatter diagram. b) Calculate the sample regression line and describe what the coefficients tell you about the relationship between the two variables.

Answer 1

a) Draw the scatter diagram.

The required scatter diagram is given as below:

b) Calculate the sample regression line and describe what the coefficients tell you about the relationship between the two variables.

The regression model for the prediction of dependent variable overweight based on the independent variable number of TV hours per week is given as below:

Regression Statistics
Multiple R	0.876196547
R Square	0.767720389
Adjusted R Square	0.749852726
Standard Error	3.825235201
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	628.7118169	628.7118169	42.96703007	1.83945E-05
Residual	13	190.2215165	14.63242434
Total	14	818.9333333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-24.70901151	4.748056533	-5.204026393	0.000169897	-34.96656401	-14.45145902
Television	0.9674474	0.147590938	6.554924109	1.83945E-05	0.648596563	1.286298236

The required regression equation is given as below:

y = a + bx

y = -24.70901151 + 0.9674474*x

Overweight = -24.70901151 + 0.9674474*number of television hours

Where, y-intercept is given as -24.70901151 and slope is given as 0.9674474.

The slope is positive which indicate a positive linear relationship between given two variables.

There is a 0.9674 increase in the overweight pounds as there is one hour increment in television hours.

If there is zero number of television hours, regression equation suggest a decrement in weight as 24.71 pounds.