Question

a. 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]

b. 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]

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

[1.5 points]

EDUCATION	AGE	GENDER	INCOME (in $1000)
12	60	female	6.5
16	39	male	120
16	33	female	21.75
12	51	male	82.5
16	42	female	55
14	20	male	7.5
14	57	male	37.5
13	61	female	5.5
16	31	male	9
12	30	male	37.5
14	68	female	13.75
16	50	male	32.5
12	27	male	0.5
16	30	male	55
18	65	female	55
19	36	male	67.5
12	22	male	21.75
6	35	male	21.75
12	67	female	9
12	48	male	23.75
12	48	female	45
15	42	male	120
14	61	female	37.5
13	34	male	82.5
17	53	male	82.5
12	39	male	67.5
16	61	male	175
18	34	male	100
12	39	female	45
14	32	male	37.5
16	54	female	45
14	55	female	13.75
14	62	male	32.5
6	39	male	16.25
12	30	female	32.5
12	35	female	16.25
16	55	male	175
17	43	male	175
16	71	male	100
16	55	male	100
14	68	female	45
11	47	male	82.5
16	30	male	55
16	38	female	100
16	41	female	45
20	62	female	120
20	49	male	67.5
16	52	female	100
16	52	male	82.5
14	33	male	82.5

Answer 1

a. To perform regression analysis in excel, click on Data > Data Analysis > Regression (Note: If data analysis option is not available then you have to add the Analysis Toolpack add-in for that click on File > Options > Add-ins > Go check on Analysis Toolpack) Ashish Kavita Data B5.- File Home Insert Page Layout Formulas a From Text/CSWD Recent Sources From Web Existing Connections Date From Table/Range GeTransform Data Review View Help Queries & Connections Book1 - Excel Tell me what you want to do Clear E Filter Test to Advanced Columns Sort & Fiter Data Tools Data Analysis S ente 1 Sort What If Forecast Analysis Sheet Forecast Group - Ungroup Subtotal Outline Queries & Connections Analysis C D E F G H I J K L M N O P Q R A 1 AGE B INCOME (in $1000) 65 120 21.75 82.5 Data Analysis Analyse Tools F.Test Two-Sample for Variances Fourier Analysis 37.5 5.5 Moving Average Random Number Generation 37.5 Lee 13.75 32.5 tret Ped two Sample for Means t-Test Two-Sample Assuming Equal Variances 05 67.5 21.75 21.75 Select Response variable for Input Y Range (Income) (I don't see HRS1 variable in data so, 1 am assuming HRS1 is referred to Income) and explanatory variable for Input X Range (Age) make sure to check on Labels if you are selecting the column headings with data Regression Input Input Y Range: OK $B$1:B$51 1 Cancel Input X Range: SA$1:$A$511 Help Labels Confidence Level: Constant is Zero 95 % Output options O Qutput Range: O New Worksheet Ply: New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

click OK, you will get output in the new sheet 1 SUMMARY OUTPUT Regression Statistics 4 Multiple R 0.162769062 5 R Square 0.026493767 6 Adjusted R Square 0.006212388 7 Standard Error 44.65305486 8 Observations 50 10 ANOVA df MSE Significance F 0.258732626 12 Regression 13 Residual 14 Total 1 48 49 SS 2 604.64522604.6452 1.30630991 95706.9748 1993.895308 98311.62 17 Intercept 18 AGE Coefficients Standard Error Stat P-value 34.27268012 22.73927931 1.507201687 0.138312739 0.546091861 0.477796092 1.142939154 0.258732626 Lower 95% Upper 95% Lower 95.0% Upper 95.0% -11.44770521 79.99306546 -11.44770521 79.99306546 -0.414581568 1.50676529 -0.414581568 1.50676529 The output gives p-values for t and F test for significance relationship between HRS1 and age, which both are same because we have only one independent variable sot and F test are equivalent (t?n distribution follows F1,n distribution) The hypothesis for these tests are Ho: B1 = 0 (there is no significant relationship between HRS1 and age) vs Ho: B1 + 0 (there is significant relationship between HRS1 and age) From the output, p-value = 0.2587 and given level of significance a = 0.05. Sincep value > a, we fail to reject Ho: B1 = 0. Hence there is no significant relationship between HRS1 and age. b. From the output, R Square value is 0.0265 which means 2.65% of variation in response variable is explained by the explanatory variable, which is very low hence regression equation does not provide good fit. C. From the regression output, regression coefficients are 34.2727 and 0.5461, so the equation of regression equation would be Y = 34.2727 + 0.5461X To predict the HRS1 for a 60 year old individual, plug X = 60 in regression equation Y = 34.2727 + 0.5461(60) = 67.04 For a 60 year old individual the HRS1 would be 67.04 thousands Don't forget the rate the answer, if it was helpful!