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]

d. Interpret the slope coefficient b₁(the coefficient for the independent variable, age). [1.5 points]

e. 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.[3.5 points]

f. 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, R²was reported with your output.  [2.5 points]

7. Use the estimated regression equation to predict the HRS1 for a 60 year old individual.

[1.5 points]

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

Book 1 - Excel (Product Activation Failed) POWERPIVOT FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW No P a SUMMARY OUTPUT Regression Statistics Multiple R 0.409779 R Square 0.167919 Adjusted R Square 0.075466 Standard Error 19.71397 Observations scatter plot O ANOVA of SS MS F gnificance F 1 705.8711 705.8711 1.816257 0.210702 9 3497.765 388.6406 10 4203.636 Regression Residual Total HRS1(Y) Predicted Y Coefficientsandard Ernt Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% 57.1708 15.97878 3.577919 0.00595 21.02428 93.31732 21.02428 93.31732 -0.44691 0.331612 1.34769 0.210702 -1.19707 0.303249-1.19707 0.303249 Intercept X Variable 1 100 50 Age(x) RESIDUAL OUTPUT Observation Predicted y Residuals 1 31.25013 0.749871 2 46.445 -0.445 3 42.86974 2.86974 Sheet1 Sheet2

There is no relation between (uang scatter plot.) HRSi d age. c) be = 57.1708 b= -0.44691 Regression can HRS1 = 57.1704 - 0.44691 (Age) d) As age increased by I unit, there will --04569 times decrease in HRS f-test for overall significance Ho - model with no independent variables fit the data as well as your modd Hp : Your model good fits data that intercept only model Here significance F70.05 - Accept Regeet Ho. Model not good fit for clata. T-test Ho: B,=0 VS Hiißto. pralue=0.210 >0.05 model regression coeff is insignificant. f) R-square 0 1679 <0.80 Regression mode not good fit for data. Estimated regression equation for 60 years HRS1 = 57.1704-0.44691(60) HRS1 =