Math 2209 Section Review Assignment: Regression NAME: 1. We have data from n 14

Question

Math 2209 Section Review Assignment: Regression NAME: 1. We have data from n 14 engineers. The variables X - age (in years) and Y - annual salary (in dollars), are recorded for each engineer. The output below is for a regression of salary on age. Regresaion Analyeis: Engsalary veraus Model Summary Enghge Fitted Line 3712.47 Regression Equation Engsalary 22480 1283 Engage (a) 3pt State the value of R2 (r-squared or R-Sq). Interpret this value in the context of the problem. (b) I pt Find the value of the coprelation coficient but do not interprer (ust give the value) HINT use the value of R-Sq to help calculate the correlation! (c) 1 pt State the equation of the regression line from the output above. Use this equation to calculate the predicted salary for the 34 year old engineer (d) 1 ptCalculate the value of the residual (i.e. error) for this 34 year old engineer who earned $61200, then indicate the residual on the plot. e) 4 pt State the value of the slope of the regression line. Then give an interpretation of the value of the slope, in the context of the problem.

Explanation / Answer

a)
R^2 = 0.909
this model account for 90.9 % of variability in Eng_Salary

b)
r = sqrt(R^2) = sqrt(0.909)

c) y^ = 22480 + 1283 * age
when age = 34
y^ = 22480 + 1283 * 34 = 66102

d)
residual = yi-yi^ = 61200 -66102
= -4902

e) slope = 1283
this means on average when age increases by 1 year, salary increase by 1283

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