A regression analysis was conducted to examine the factors influencing income (m

Question

A regression analysis was conducted to examine the factors influencing income (measured in thousands of dollars). The model contains a variable for age (in years), years of education, a categorical variable for sex (women=1; men are the reference category), and a categorical variable for race (dummy variables are used for White and Black; All Other Races are the reference category). The results from the regression analysis are below:

The mean for each independent variable is:

Use the information from the table to answer the questions below. Please keep your answers brief–you do not need to write a lot to answer these questions.

a) Doesthisregressionmodelsignificantlyimproveourabilitytopredictyrelativeto just guessing the mean? Justify your answer by drawing on the appropriate statistic(s) in the table. (5 points)

b) InterpretthevalueofR2fromthetable.(5points)

c) Pickonepartialslopeandstatethenullandresearchhypothesesforit.(5points)

d) Whatgroupdoestheinterceptreferto?(5points)

e) Pick one interval-ratio variable and interpret the partial slope. (10 points)

f) Pickonedummyvariableandinterpretthepartialslope.(10points)

Explanation / Answer

(a) Since the p- value < 0.01, the regression is significant. The model significantly improve our ability to predict y relative to just guessing the mean

(b) R^2 = 0.372 means about 37.2% of the variation in y is explained by the model in terms of variation in x

(c) Slope for Age is 0.09. This means the income increases by $90 for every one year increase in Age

(d) The intercept is not meaningful in the context of this problem.

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