Question

Question 12

Please answer the following set of questions, based on the information provided below.

The data listed below give information for 10 middle-level managers at a particular company. The first column is years of experience [X] and the second column is annual salary (in thousands) [Y]. We are going to examine the relationship between salary in thousands [Y] and years of experience[X]. Below is the regression output.

Manager#	(X)	(Y)
1	xx	66
2	xx	69
3	23	78
4	xx	41
5	19	xx
6	15	xx
7	24	xx
8	xx	33
9	2	28
10	xx	32

SUMMARY OUTPUT
Regression Statistics
Multiple R	xxx
R Square	0.789
Adjusted R Square	0.740
Standard Error	8.376
Observations	10

ANOVA
	df	SS	MS	F	SignificanceF
Regression	1.000	1503.75	1503.75	xxxx	xxxx
Residual	8.000	561.25	70.156
Total	xxx	xxx
	Coefficients	Standard Error	t Stat	P value
Intercept	16.586	7.201	2.303	0.050
Yrs Exp (X)	2.892	0.625	xxx	0.003

RESIDUALOUTPUT
Observation	Standardized Residuals
1	-0.956
2	2.129
3	-0.567
4	-1.307
5	1.381
6	-0.417
7	-2.780
8	-0.962
9	1.734
10	1.377

According to the least squares line, if the experience increases by 2 years, the Salary should _______ by ______units (in thousands).

Answer 1

Solution

Back-up Theory

The linear regression model: Y = β₀ + β₁X + ε, ……………………..............................................................…………………..(1)

where ε is the error term, which is assumed to be Normally distributed with mean 0 and variance σ².

Estimated Regression of Y on X is given by: Y_cap = β_0cap + β_1capX, ………….......................................................………….(2)

In the estimated regression of Y on X given by: Y = β_0cap + β_1capX,

β_0cap represents the y-intercept mathematically and physically represents the expected value of the response (dependent) variable when the predictor (independent/explanatory) variable is zero …............................................………(3a)

β_1cap represents the slope of the regression line mathematically and physically represents the expected change (increase/decrease) in value of the response (dependent) variable when the predictor

(independent/explanatory) variable changes (increases/decreases) by one unit…………….......................................….. .. (3b)

Now, to work out the solution,

From the given regression output, estimated regression line is:

Annual salary (in thousands) [Y] = 16.586 + 2.892 x years of experience [X]…………………………… (4)

Vide (2), in (4), β_0cap = 16.586 and β_1cap = 2.892.

So, vide (3b),

If the experience increases by 2 years, the Salary should increase by (2 x 2.892) = 5.784 units (in thousands).

Answer

DONE