Question

The United States of America has long been viewed as a land of opportunity where everyone is positioned to succeed. Stratification scholars have long argued that opportunity is limited based on the social class one was born into. An individual born into a higher social class background is likely to have more opportunities that one born into a lower social class background. This is believed to be true in post-zombie US as well. To explore this, please see the data from the New Reformed U.S. Census Bureau below comparing the percentage of state residents with a Bachelor’s degree with state median household income collected in 2013. This data represents the 10 most populated states in the Reformed U.S.

State	Percentage of State Residents with a Bachelor’s Degree	Median Household Income (x$100)
California	29.80	566.45
Texas	22.50	449.22
New York	32.30	513.84
Florida	27.20	455.95
Illinois	31.20	520.06
Pennsylvania	26.60	452.59
Ohio	23.30	471.82
Michigan	26.10	471.82
Georgia	28.10	468.32
New Jersey	35.60	644.70

1. What is the r value for the relationship between the data distributions above?

2. What is the proportion of variance accounted for?

3. You will need to find the regression line for this data. With that in mind, what is the b for this data?

4. What is the a for this data?

5. Using the data above, what is the Y' for an X of 24.8?

6. Using the data above, what is the Y' for an X of 27.65?

7. In your own words but based on the strength and direction of the relationship you calculated, explain the relationship between education and median household income.

Answer 1

Ans:

State	Percentage of State Residents with a Bachelor’s Degree	Median Household Income
California	29.8	566.45
Texas	22.5	449.22
New York	32.3	513.84
Florida	27.2	455.95
Illinois	31.2	520.06
Pennsylvania	26.6	452.59
Ohio	23.3	471.82
Michigan	26.1	471.82
Georgia	28.1	468.32
New Jersey	35.6	644.7
Average	28.27	501.477
SD	4.049	62.614
r	0.834
slope,b	12.895
intercept,a	136.94

a=y-bar-b*x-bar

a)r=0.834

b)Proportion of variance accounted for =0.834^2=0.695 or 69.5%

c)slope,b=r*sy/sx=12.895

d)intercept,a=y-bar-b*x-bar=136.94

Regression equation:

y'=136.94+12.895 x

e)when x=24.8

y'=136.94+12.895*24.8=456.74

f)when x=27.65

y'=136.94+12.895*27.65

y'=493.49

g)There is strong positive relationship between education and median household income.