A social scientist would like to analyze the relationship between educational at

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 36 56 35 72 47 107 52 Click here for the Excel Data File a. Find the sample regression equation for the model: Salary = 0 + 1Education + . (Round intermediate calculations to at least 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)    + Education    b. Interpret the coefficient for Education. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,000. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $7,000. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $7,000. As Education inceases by 1 unit, an individual’s annual salary is predicted to decrease by $8,000. c. What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)     $    rev: 11_14_2015_QC_CS-31836

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Salary
Independent Variable: Education
Salary = 27.625 + 7 Education
Sample size: 8
R (correlation coefficient) = 0.71285611
R-sq = 0.50816383
Estimate of error standard deviation: 18.220295

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Regression equation:

Salary = 27.63 + 7 (Education)

b) As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $7,000.

c) For Education = 7,

Salary = $ 76625

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 27.625 12.960156 0 6 2.1315329 0.077 Slope 7 2.8114526 0 6 2.4898161 0.0472

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