Question

a. Develop a scatter plot with HRS1 (how many hours per week one works) as the dependent variable and age as the independent variable. Include the estimated regression equation and the coefficient of determination on your scatter plot. [ 1.5 points]

b. Does there appear to be a relationship between these variables (HRS1 and age)? Briefly explain and justify your answer.[ 1 point]

c. Calculate the slope (b₁) and intercept (b₀) coefficients and use them to develop an estimated regression equation that can be used to predict HRS1 given age.Conduct your analysis using Alpha (α ) of  0.05. Submit your Excel output or workings to receive full points. Hint: Use formulas and Excel, or Excel regression Tool (run a regression with HRS1 as dependent or y variable and age as independent or x variable).  [10 points]

Interpret the slope coefficient b₁(the coefficient for the independent variable, age).

Age	HRS1
58	32
24	46
32	40
29	40
34	86
49	40
60	40
78	25
39	5
67	15
22	40

Answer 1

a)

90+ 811 y = 57.1708 -0.4469x | + 102030405060708090

b)

There exists a negative correlation but it appears to be neither weak nor strong relationship between x and y.

Here as value of 'x' increases value of 'y' decreases but the change is not significantly associated. Estimated regression line is passing through only two points and rest of the points are dispersed widely around the line. Still there are many points close to the line and few points behaving as outliers. Hence association seems neither too strong nor too weak. It is moderate.

c)

Analysis done using Excel regression tool at 0.05 level of significance:

SUMMARY OUTPUT
Regression Statistics							1
Multiple R	0.409779396
R Square	0.167919153
Adjusted R Square	0.075465726
Standard Error	19.7139694
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	705.8710586	705.8710586	1.816256659	0.210701652
Residual	9	3497.765305	388.6405895
Total	10	4203.636364
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	57.17079946	15.97878443	3.57791919	0.00595008	21.02427788	93.31732105	21.02427788	93.31732105
X Variable 1	-0.446908118	0.331611539	-1.347685668	0.210701652	-1.197065534	0.303249298	-1.197065534	0.303249298

bo = 57.1708, b1 = -0.4469

Equation of regression line:

y = 60 +612 y = 57.1708 - 0.4469.r

Slope coefficient of -0.4469 indicates that per unit change in 'x' (age of a person) causes average of -0.4469 units of change in 'y' (HSR).

Since p-value = 0.2107 > 0.05 this association is statistically significant.