Question

City	Population	% incomes below $5,000	% unemployed	Murders per million inhabitants per year
1	587000	16.5	6.2	11.2
2	643000	20.5	6.4	13.4
3	635000	26.3	9.3	40.7
4	692000	16.5	5.3	5.3
5	1248000	19.2	7.3	24.8
6	643000	16.5	5.9	12.7
7	1964000	20.2	6.4	20.9
8	1531000	21.3	7.6	35.7
9	713000	17.2	4.9	8.7
10	749000	14.3	6.4	9.6
11	7895000	18.1	6	14.5
12	762000	23.1	7.4	26.9
13	2793000	19.1	5.8	15.7
14	741000	24.7	8.6	36.2
15	625000	18.6	6.5	18.1
16	854000	24.9	8.3	28.9
17	716000	17.9	6.7	14.9
18	921000	22.4	8.6	25.8
19	595000	20.2	8.4	21.7
20	3353000	16.9	6.7	25.7

1-What percentage of the differences in murder rates can we explain using % of population with incomes below $5,000?

a).50%

b)25.6%

c)84%

d)71

Is this correlation significant in the population?

a)yes

b) no

2-Now let's look at the correlation between the % of unemployed people and murders per year. calculate r

a)70.7

b).86

c).73

d).75

3-Would this correlation be significant in the population?

a)yes

b)no

4-If we knew that % unemployed for a city was 6.0 what would we predict the murders per million inhabitants per year should be?

a)7.09

b)21.03

c)57.8

d)13.95

5-If we knew that % unemployed for a city was 10.0 what would we predict the murders per million inhabitants per year should be?

a)42.3

b)26.3

c)73.4

d)68.8

Answer 1

Solution:

1-What percentage of the differences in murder rates can we explain using % of the population with incomes below $5,000?

Answer:

The correct option is d) 71%

Explanation:

We can use the excel regression data analysis tool to find the coefficient of determination. The excel output is given below:

SUMMARY OUTPUT Regression Statistics 71% 69% 5.51 20 R Square diusted R Square Standard Error Observations ANOVA Significance F MS Regression Residual Total 11308.339479 1308.339479 43.06404212 3.63753E-06 18546.8625208 30.38125115 19 1855.202 Coefficients Standard Error 29.901162567.789184063 -3.838805492 2.559389582 P-value Lower 95% Upper 95% t Stat Intercept % incomes below $5,000 0.00120 -46.26563101-13.53669411 0.390012927 6.56231987 0.000 .740002829 3.378776335

Is this correlation significant in the population?

Answer: a) yes

Because the p-value is less than the significance level.

2- Now let's look at the correlation between the % of unemployed people and murders per year. calculate r

Answer: b. 0.86

Explanation:

Using the excel regression data analysis tool, we have the below results:

SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Square Standard Error Observations Correlation coefficient 0.86 0.75 0.73 5.10 20 ANOVA Significance F MS Regression Residual Total 1387.5997 467.6023 1855.2020 1387.5997 53.4146 0.0000 18 25.9779 19 Intercept Slope oefficients Standad ErrortStat P-value Lower 95% Upper 95% 6.8137 Intercept % un 28.5267 -4.1867 0.0006 42.8418 5.0445 -14.2116 7.3085 9.1147 7.0796 0.9687 0.0000 employed

3-Would this correlation be significant in the population?

Answer: a) Yes

Because the p-value is less than the significance level.

4-If we knew that % unemployed for a city was 6.0 what would we predict the murders per million inhabitants per year should be?

Answer: The answer is d) 13.95

Explanation: Using the regression equation, we have:

$\hat{y}=-28.5267+7.0796 \times 6$

  $=13.95$

5-If we knew that % unemployed for a city was 10.0 what would we predict the murders per million inhabitants per year should be?

Answer: The answer is a) 42.3

Explanation: Using the regression equation, we have:

$\hat{y}=-28.5267+7.0796 \times 10$

  $=42.3$