Question

The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y = 1.402x-12.106. Complete parts (a) and (b) below. 766 Average Weekly Wages (state), x Average Weekly Wages (federal), y 745 995 794 1111 802 1140 842 1207 887 1244 932 1276 951 1303 1048 (a) Find the coefficient of determination and interpret the result. 2 = 0.944 (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? that can be explained by the variation in average weekly wages for and is represented by The remaining fraction of the variation, The coefficient of determination is the fraction of the variation in average weekly wages for . is unexplained and is due to other factors or to sampling error. (b) Find the standard error of estimates, and interpret the result. (Round to two decimal places as needed.) How can the standard error of estimate be interpreted? The standard error of estimate of the average weekly wage for for average weekly wage for is about se dollars.

Answer 1

For the given data using Regression in Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.971652465
R Square	0.944108513
Adjusted R Square	0.934793265
Standard Error	28.22118098
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	80719.38966	80719.39	101.3509	5.57451E-05
Residual	6	4778.610337	796.4351
Total	7	85498
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-12.10615245	117.3979573	-0.10312	0.921228	-299.368605	275.1563001
x	1.402120735	0.139274517	10.06732	5.57E-05	1.06132827	1.742913201

So from the above output

y?=0.944) Interpretation: 1st blank - Federal government employees and blank state government employees god blank g 4th blank s inge Se= (28.22 Interpretation: yst blank - federal govermend employees and blank - a specific god blank - state government employees