Question

A company wants to know how job performance relates to IQ. They collect data on 30 employees, resulting in the following table. Enter the data into SPSS OR EXCEL with appropriate variable labels. Show all syntax and output. (5pts)

1. 1. Find the equation that best represents the linear relationship between X and Y.
   2. Determine the strength of this relationship.
   3. Test the null hypothesis that, in the population from which the sample was drawn, the slope of the prediction line is zero.

Name	Job Performance	IQ
Henry	85	109
Riley	84	106
Alexis	87	125
Evelyn	69	84
Blake	69	89
Dominic	81	109
Jose	71	121
Tristan	76	102
Kayden	77	111
Makayla	76	106
Ella	90	107
Piper	74	97
Jonathan	74	133
Joshua	65	96
Brooklyn	66	97
Connor	73	116
Sadie	80	108
Zoe	96	102
Cameron	77	94
Jason	73	98
Logan	70	87
Olivia	68	104
Madison	66	85
Lucas	86	145
Tyler	88	105
Madeline	82	96
Michael	85	103
Mason	78	115
Andrew	87	135
Joseph	72	104

Answer 1

Using an excel tool of data analysis of linear regression we get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.440888
R Square	0.194382
Adjusted R Square	0.16561
Standard Error	7.412171
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	371.1723	371.1723	6.75592438	0.014742959
Residual	28	1538.328	54.94027
Total	29	1909.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	51.27493	10.17996	5.036851	2.50752E-05	30.42223226	72.12763
IQ	0.246708	0.094916	2.599216	0.014742959	0.052280775	0.441135

a) Since Intercept=51.2749 and Slope =0.2467

hence equation will be

y=0.2467*IQ+51.2749

b) The strength of the relationship is the R-value which is 0.4409

c) The hypothesis is

Ho: Slope=0

Ha: Slope 0

Since the p-value calculated for the test is 0.015 at 95 % confidence level which is less than the level of significance (0.05) hence we reject the null hypothesis and conclude that the slope is non zero value.