Question

Salary	Education
42	6
48	7
82	1
46	3
67	1
54	5
105	6
42	0
38	4
56	6
90	2
44	7
67	5
64	7
143	12
43	0
76	7
64	4
127	6
42	0

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

a. Find the sample regression equation for the model: SalaryˆSalary^ = β₀ + β₁Education + ε. (Round answers to 2 decimal places.)

b. Interpret the coefficient for Education.

• As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $4,530.
• As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $8,590.
• As Education increases by 1 year, an individual’s annual salary is predicted to increase by $8,590.
• As Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,530.

c. What is the predicted SalaryˆSalary^ for an individual who completed 8 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

Answer 1

A)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	89.00	1340.00	184.95	16586.00	837.00
mean	4.45	67.00	SSxx	SSyy	SSxy

sample size ,   n =   20      
here, x̅ = Σx / n=   4.450          
ȳ = Σy/n =   67.000          
SSxx =    Σ(x-x̅)² =    184.9500      
SSxy=   Σ(x-x̅)(y-ȳ) =   837.0      
              
estimated slope , ß1 = SSxy/SSxx =   837/184.95=   4.525547      
intercept,ß0 = y̅-ß1* x̄ =   67- (4.5255 )*4.45=   46.861314      
              
Regression line is, Ŷ=   46.86   + (   4.53   )*x

..................

B)

• As Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,530.

.................

C)

Predicted Y at X=   8   is          
Ŷ=   46.8613   +   4.5255   *8=   83

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