Question

1. Describe how to use a simple (bivariate) regression model to carry out a difference in the means test, to estimate a descriptive statistic, and to estimate an unbiased (or less biased) causal effect.

Answer 1

Solution ) SIMPLE BIVARIATE REGRESSION

Here we consider a Case Study to describe bivariate Regression Analysis in SPSS.

we have 2 variables one independent and one dependent Variable.

Years= independent variable

Salary=dependent variable.

H0 = there is not significance difference of independent variable on dependent variable.

H1=there is significance difference of independent variable on dependent variable.

After entering data in spss in Variable view

name = years , salary

type= numeric

measure= scale

to get data in output of SPSS

Analyse - Reports - Case Summaries

then select both variables years and salary in variable group then click Ok

we get,

Case Processing Summarya
	Cases
	Included		Excluded		Total
	N	Percent	N	Percent	N	Percent
Number of years in employement	50	100.0%	0	0.0%	50	100.0%
Salary in rupees	50	100.0%	0	0.0%	50	100.0%
a. Limited to first 100 cases.

Case Summariesa
		Number of years in employement	Salary in rupees
1		1.00	35000.00
2		1.00	15000.00
3		1.00	26000.00
4		1.00	37000.00
5		1.00	38000.00
6		2.00	27000.00
7		2.00	45000.00
8		2.00	50000.00
9		2.00	36000.00
10		2.00	40000.00
11		3.00	45000.00
12		3.00	40000.00
13		3.00	38000.00
14		3.00	6000.00
15		3.00	46000.00
16		4.00	30000.00
17		4.00	32000.00
18		4.00	62000.00
19		4.00	45000.00
20		4.00	21000.00
21		4.00	55000.00
22		4.00	47000.00
23		5.00	50000.00
24		5.00	39000.00
25		5.00	46000.00
26		5.00	50000.00
27		6.00	44000.00
28		6.00	46000.00
29		6.00	3000.00
30		7.00	55000.00
31		7.00	56000.00
32		7.00	46000.00
33		8.00	57000.00
34		8.00	40000.00
35		9.00	55000.00
36		9.00	53000.00
37		9.00	44000.00
38		10.00	80000.00
39		10.00	65000.00
40		12.00	69000.00
41		12.00	65000.00
42		13.00	82000.00
43		14.00	85000.00
44		14.00	80000.00
45		14.00	65000.00
46		15.00	57000.00
47		17.00	59000.00
48		19.00	70000.00
49		20.00	96000.00
50		22.00	95000.00
Total	N	50	50
a. Limited to first 100 cases.

Assumptions : (1) Linearity=Relationship between dependent and independent variable should be linear.

(2) Constant Variance of Error terms .

(3)Error terms should be Independent of each Other.

(4) Error terms should be normally distributed.

First of all we have to check linearity of given data.

this looks like positive correlation between salary and number of years.

now,we have to perform regression.

Now interpret ,OUTPUT of SPSS

we know ,

regression equation is given as : Y = a + b X

where Y = dependent variable

a= Intercept , b= Slope , X=Independent variable.

Descriptive Statistics
	Mean	Std. Deviation	N
Salary in rupees	49360.0000	20003.83637	50
Number of years in employement	7.0400	5.40959	50

Correlations
		Salary in rupees	Number of years in employement
Pearson Correlation	Salary in rupees	1.000	.780
	Number of years in employement	.780	1.000
Sig. (1-tailed)	Salary in rupees	.	.000
	Number of years in employement	.000	.
N	Salary in rupees	50	50
	Number of years in employement	50	50

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.780a	.608	.599	12660.07854
a. Predictors: (Constant), Number of years in employement
b. Dependent Variable: Salary in rupees

ANOVAa
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	11914195742.022	1	11914195742.022	74.335	.000b
	Residual	7693324257.978	48	160277588.708
	Total	19607520000.000	49
a. Dependent Variable: Salary in rupees
b. Predictors: (Constant), Number of years in employement

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	29067.173	2957.252		9.829	.000
	Number of years in employement	2882.504	334.329	.780	8.622	.000
a. Dependent Variable: Salary in rupees

from above table , we have seen

a=29067.173

b=2882.504

and p-value =0.000<0.05 reject H0.

means there is statistically significance difference .

and conclude that Independent variable is sufficient to explain dependent variable .

Y=29067.173 + 2882.504*(number of years)

now we can predict any number of year salary.

Residuals Statisticsa
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	31949.6758	92482.2578	49360.0000	15593.16683	50
Residual	-43362.19531	22107.78906	.00000	12530.22815	50
Std. Predicted Value	-1.117	2.765	.000	1.000	50
Std. Residual	-3.425	1.746	.000	.990	50
a. Dependent Variable: Salary in rupees