Question

The table shows the avrage wookly wages (n dollars) for state govemment eplnyeesand deral govemment employees for 8 yeans. The equation of the regression line is y 1.479x-78 874 Complete parts (a) and (b) below Weekly Wages ( 794 (a) Find the coefficient of deteemination and intepret the resu Round to three decimal places as needed. How can the ooefficient of determination be interpreted? The coeficient of deseminasion is the fraction ol the variation in average weekly wages for he variation in average weekly wages for that can be explained by ▼ is unexplained and is due to other factors or to sanoegenor. (b) Find the standard emor of estimane s, and interpeet the resut Round to two decimal places as needed How can the standard emor of estimate be interpreted? The standard ersor of estimate of the average weekly wage for average weekly wage for is abouts,dollars Enter your answer in each of the answer boxes The table shows the average weekly wages (in dollars) for state govenment employees and federal government employees for 8 years. The equation of the regression line is y 1.479x-78.874. Complete parts (a) and (b) below. e Weekly Wages (state), x e Weekly Wages( 758 1001 794 1106 808 1153 836 876 935 943 D 1305 1037 200 249 265 (a) Find the coefficient of determination and interpret the result (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? The coefficient of determination is the fraction of the variation in average weekly wages for the variation in average weekly wages for that can be explained by and is represented by The remaining fraction of the variation, . is unexplained and is due to other factors or to sampling error (b) Find the standard error of estimate se 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 Y for average weekly wage for is about se dollars.

Answer 1

data

x	y
758	1001
777	1037
794	1106
808	1153
836	1200
876	1249
935	1265
943	1305

Using Excel

data -> data analysis -> regression

result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9470
R Square	0.8967
Adjusted R Square	0.8795
Standard Error	38.1983
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	76029.3564	76029.3564	52.1068	0.0004
Residual	6	8754.6436	1459.1073
Total	7	84784.0000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-78.8740	172.7768	-0.4565	0.6641	-501.6438
x	1.4787	0.2048	7.2185	0.0004	0.9774

a)
r^2 = 0.897

federal
state
R^2
1- R^2

b)
Se = 38.2

federal government
specific
state government

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