Question

The data below are for the number of unemployed persons (in millions) and the federal unemployment insurance payments (in billions of dollars) for the years 2010 – 2017. Some economists state that these two variables are positively related, and that the amount of federal unemployment insurance payments can be used to predict the number of unemployed persons.

	Year
	2010	2011	2012	2013	2014	2015	2016	2017
Federal Unemployment Insurance Payments	11.8	10.7	18.0	19.7	23.7	31.5	18.4	16.8
# of Unemployed Persons	6.2	6.1	7.6	8.3	10.7	10.7	8.5	8.3

Assume that a simple linear regression model is appropriate for these data. You can do the calculations manually, or use a statistical software package (e.g., Excel) to conduct a least squares regression analysis. Make sure to check your data entry, as any errors will automatically make all of your answers incorrect! Conduct the appropriate t-test at α = .05 to determine whether the amount of federal unemployment insurance payments is a useful predictor of the number of unemployed persons.

The critical value for rejecting the most obvious H₀ is (Click to select)±+- . (Report your answer to 3 decimal places, using conventional rounding rules)

The value of the test statistic is (Click to select)+-± . (Report your answer to 2 decimal places, using conventional rounding rules)

Should the most obvious null hypothesis be rejected? (Click to select)noyescannot be determined from the information provided

Can you conclude that the amount of federal unemployment insurance payments is a useful predictor of the number of unemployed persons. (Click to select)nocannot be determined from the information providedyes

What is the correlation between the independent and dependent variables for this simple linear regression analysis?  (Negative values must include the minus sign. Report your answer to 2 decimal places, using conventional rounding rules.)

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.932702
R Square	0.869932
Adjusted R Square	0.848254
Standard Error	0.679515
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	18.52956	18.52956	40.12981	0.000724
Residual	6	2.770443	0.461741
Total	7	21.3
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	3.663917	0.770267	4.756684	0.003137	1.779141
x	0.246273	0.038876	6.334809	0.000724	0.151146

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Yes

Yes, it is a good predictor

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