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. What is the predicted salary for an individual who completed 7 years of higher education? (Do not round the Excel coefficients-use all the decimal places Excel gives you. Round your final answer to a whole number, and express in thousands of dollars. If your final answer was 67.95328102, you would round to a whole number, 68, and express the salary in thousands of dollars: 68,000. Do NOT include the dollar sign in your answer.)

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
3	40	1.00	415.14	20.38
4	53	0.00	54.39	0.00
6	80	4.00	385.14	39.25
2	42	4.00	337.64	36.75
5	70	1.00	92.64	9.63
4	50	0.00	107.64	0.00
8	110	16.00	2462.64	198.50
0	38	16.00	500.64	89.50

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	32	483	42	4355.875	394.000
mean	4.000	60.375	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ = Σx / n=   4.00   ,     ȳ = Σy/n =   60.375  
                  
SSxx =    Σ(x-x̅)² =    42.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   394.0          
                  
estimated slope , ß1 = SSxy/SSxx =   394.0   /   42.000   =   9.38095
                  
intercept,   ß0 = y̅-ß1* x̄ =   22.85119          
                  
so, regression line is   Ŷ =   22.851   +   9.381   *x
-----------------

Predicted Y at X=   7   is                  
Ŷ =   22.8512   +   9.3810   *   7   =   88.518≈ 89
predicted salary for an individual who completed 7 years of higher education = $89000