Question

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

1. 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.
2. Does there appear to be a relationship between these variables (HRS1 and age)? Briefly explain and justify your answer.
3. 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).
4. Interpret the slope coefficient b₁ (the coefficient for the independent variable, age).
5. Use t and F to test for a significant relationship between HRS1 and age. Use α = 0.05 and make sure you know what hypotheses you are using to conduct the significance tests.
6. Calculate and interpret the coefficient of determination R². Based on this R², did the estimated regression equation provide a good fit? Briefly justify your answer. Hint: If you used Excel Regression Tool to answer part c, R² was reported with your output.
7. Use the estimated regression equation to predict the HRS1 for a 60 year old individual.

Answer 1

Solution:

In excel select the data

Go to insert>chart

add axis titles using +sign

select design

You get

Soluiton-b

From correlation matrix

	Age	HRS1
Age	1
HRS1	-0.40978	1

r=-0.40978

There exists a negative relationship between age and HRS1

as age increases ,HRS1 decreases and viceversa.

Solutionc:

use Data>Data analysis >Regression

you get

Output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.409779
R Square	0.167919
Adjusted R Square	0.075466
Standard Error	19.71397
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	705.8711	705.8711	1.816257	0.210702
Residual	9	3497.765	388.6406
Total	10	4203.636
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	57.1708	15.97878	3.577919	0.00595	21.02428	93.31732
Age	-0.44691	0.331612	-1.34769	0.210702	-1.19707	0.303249

slope=b0=-0.44691

y intercept=57.1708

Regression equation is

HRS1=57.1708-0.44691*AGE

Solution-d:

slope=b0=-0.44691

As age increases by one year,HRS1(hours per week one works)decrease by 0.44691 hours