Question

Simple Linear Regression Hypothesis Test

A researcher was interested in whether there was a positive predictive relationship between the number of years employed at a company and the annual salary in dollars. The following data was obtained for 10 participants:

Table 1

Data for Salary/Years of Job Experience

Case	Years	Salary (x 1000 $)
1	1	27.314
2	4	61.870
3	6	42.755
4	10	78.096
5	15	54.180
6	20	95.735
7	22	94.320
8	3	45.720
9	8	38.640
10	14	85.162

Conduct the 4 steps of hypothesis testing to evaluate whether the number of years is a statistically significant positive predictor of the annual gross salary.

Answer 1

Independent variable (X) : Year

Dependent variable (Y): Salary

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.831931737
R Square	0.692110414
Adjusted R Square	0.653624216
Standard Error	14.44567609
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3752.719618	3752.719618	17.98334071	0.002834861
Residual	8	1669.420462	208.6775577
Total	9	5422.14008
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	33.27771453	8.243854961	4.036669093	0.003753084	14.26735091	52.28807814
Years	2.825386939	0.666258476	4.240676916	0.002834861	1.28899214	4.361781738

That is we have

Hypotheses are:

The test statistics is

t = 4.241

Degree of freedom: df=n-2=8

The p-value using excel function "=TDIST(4.241,8,1)" is 0.0014.

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that the number of years is a statistically significant positive predictor of the annual gross salary.