Question

Ched Exercise 14-22 (LO14-1, LO14-5) A regional planner employed by a public university is studying the demographics of nine counties in the eastern region of an Atlantic seaboard state. She has gathered the following data: 8:42 County Median Income $48,952 46, 669 47,780 46,855 37,724 35,414 34, 389 38, 128 30,384 HITIMO Median Age Coastal 48.3 58.8 48.0 39.2 51.9 56.2 49.1 30.3 38.9 nces Click here for the Excel Data File a. Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.) 0.180 The correlation of Income and Median Age Next > < Prey 14 of 25 acer,

1. Include the aspect that the county is "coastal" or not in a multiple linear regression analysis using a "dummy" variable.

2. Test each of the individual coefficients to see if they are significant.

3. What would a histogram look like of the residuals? A scatter plot?

Answer 1

I used R software to solve this question

R codes and output:

> d=read.table('data.csv',header=T,sep=',')
> head(d)
Income Age Coastal
1 48952 48.3 1
2 46669 58.8 1
3 47780 48.0 0
4 46855 39.2 1
5 37724 51.9 1
6 35414 56.2 1
> attach(d)
> cor(Income , Age)
[1] 0.1799701
> fit=lm(Income~ Age+ Coastal)
> summary(fit)

Call:
lm(formula = Income ~ Age + Coastal)

Residuals:
Min 1Q Median 3Q Max
-7453.0 -5349.8 -84.4 3927.0 10418.7

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 39669.20 14380.78 2.758 0.0329 *
Age -48.08 334.77 -0.144 0.8905
Coastal 5899.94 5768.20 1.023 0.3458
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7237 on 6 degrees of freedom
Multiple R-squared: 0.1761, Adjusted R-squared: -0.09859
F-statistic: 0.641 on 2 and 6 DF, p-value: 0.5594
> residuals=fit$residual
> residuals
1 2 3 4 5 6
5705.15192 3926.99875 10418.66818 3170.61800 -5349.75774 -7453.01094
7 8 9
-2919.44310 -84.35934 -7414.86574
> hist(residuals)

a.

Correlation between median income and median age is 0.180

2.

Since p-value for both the variables (0.8905, 0.3458) are greater than 0.05, hence we conclude that both variable are not statistically significant.

3.

histogram of residuals:

Residuals are positively skewed.