Question

A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual’s annual salary (in $1,000s):

Education 3 4 6 2 5 4 8 0

Salary 40 53 80 42 70 50 110 38

Data is in the spreadsheet.

Use the Regression tool in Data Analysis to find the sample regression equation for the model: Salary = β0 + β1Education + ε.

What is the coefficient for β1? ______ thousand. (Enter your answers in thousands rounded to 2 decimal places. The data is ALREADY in thousands. If you got 34.8763 for your answer, you would round that number to 34.88. The teacher's salary would be 34,880. This question is asking you to enter 34.88 ) (Enter your answers in thousands rounded to 2 decimal places.)

Answer 1

Line of Regression Y on X i.e Y = bo + b1 X
					X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
3	40	1	415.14	20.38
4	53	0	54.39	0
6	80	4	385.14	39.25
2	42	4	337.64	36.75
5	70	1	92.64	9.63
4	50	0	107.64	0
8	110	16	2462.64	198.5
0	38	16	500.64	89.5

calculation procedure for regression
mean of X = ∑ X / n = 4
mean of Y = ∑ Y / n = 60.375
∑ (Xi - Mean)^2 = 42
∑ (Yi - Mean)^2 = 4355.87
∑ (Xi-Mean)*(Yi-Mean) = 394.01
b1 = ∑ (Xi-Mean)*(Yi-Mean) / ∑ (Xi - Mean)^2
= 394.01 / 42
= 9.38
bo = ∑ Y / n - b1 * ∑ X / n
bo = 60.375 - 9.38*4 = 22.85
value of regression equation is, Y = bo + b1 X
Y'=22.85+9.38* X          
the coefficient for β1 =9.38