Question

A sociology professor hypothesizes that men's performance of routine housework is associated with the amount of sex they have with their partners. Data gathered using probability sampling are presented below for a group of men. Housework performance was measured as hours of routine housework performed the previous week. Sexual frequency was measured as the number of times each man reported having sex in the past year.

Weekly Household Hours	Sex Frequency per Year
14	56
8	64
20	80
3	160
12	96
19	24
9	80
15	56
8	176

a. Identify the value of the statistic that shows the strength and the direction of the relationship between the independent variable and the dependent variable?

b. Interpret the statistic that you calculated for the previous question.

c. Please calculate and write down the regression equation, then interpret the y-intercept (a) and the slope (b). (You can just use "y-hat" to indicate Y^hat.) Please make sure to show your work on your worksheet.

d. Based on the data above, what sexual frequency do you predict for a man who performs 18 hours of housework per week?

Answer 1

(a) the linear correlation between housework_per_week and sexual_frequency=r=-0.700

since the sign of the correlation coefficient is negative, so there is negative correlation between independent variable and the dependent variable

here we use sexual_frequency (y) as dependent variable and housework_per_week (x) as independent variable , as we have to predict number sexual frequency for a man who perform 18 hours of housework per week

(b) since the sign of correlation is negative, so if there is increase in housework_per_week (x) the sexual_frequency (y) will decrease and vice-versa.

(c) the regression equation =a+bx=163.1-6.3*x

a=(sum(y)*sum(x²)-sum(x)*sum(xy))/(n*sum(x²)-(sum(x))²)=(792*1544-108*7952)/(9*1544-108*108)=163.1

b=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x²)-(sum(x))²)=(9*7952-108*792)/(9*1544-108*108)=-6.3

S.N.	Weekly Household Hours	Sex Frequency per Year	x2	y2	xy
1	14	56	196	3136	784
2	8	64	64	4096	512
3	20	80	400	6400	1600
4	3	160	9	25600	480
5	12	96	144	9216	1152
6	19	24	361	576	456
7	9	80	81	6400	720
8	15	56	225	3136	840
9	8	176	64	30976	1408
sum=	108	792	1544	89536	7952
n=	9	9	9	9	9

here intercept is 163.1,it means if a person don't perform housework_per_week (i.e. x=0),his sexual frequency will be 163.1.

(The intercept is the expected mean value of dependent variable Y when all X=0.)

the slope=-6.3 this imply additional hour housework_per_week will decrease the sexual frequency by 6.3.

slope change in dependent variable when unit change is done in independent variable

(d) predicted sexual frequency predict for a man who performs 18 hours of housework per week=49.6.

using the regression equation in part (a)

for x=18, the =163.1-18*6.3=49.7

the regression analysis can be done using ms-excel as given

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.699673
R Square	0.489542
Adjusted R Square	0.41662
Standard Error	38.03661
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9712.516	9712.516	6.713179	0.035893
Residual	7	10127.48	1446.783
Total	8	19840
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	163.0968	31.63576	5.155456	0.001316	88.29008	237.9035	88.29008	237.9035
X Variable 1	-6.25806	2.415327	-2.59098	0.035893	-11.9694	-0.54672	-11.9694	-0.54672