Question

4. Recent data on crime rates and education for 41 Florida counties are graphed in the scatter plot below. Here, CRIME crimes per 1000 residents and EDUC percentage of 25+ year olds who have at least a high school degree. The LSQ line for predicting CRIME using EDUC is CRIME =-42.9 + 1.44 EDUC (see the scatterplot below) a. Circle the point in the scatterplot that corresponds to the first observation (EDUC(countyl), CRIME(county1)) (75.2, 41.3). b. Verify that the residual corresponding to the first observation (EDUC(county), CRIME(county)) (75.2,41.3) is -24.1. Do the numerical computations. c. Based on this best-fit ne, what is the predicted CRIME rate for a county with 20% high school graduation rate? Explain why this prediction is ill- advised. d. It turns out tha20.234. Interpret this value in the words of the problem. Would you say EDUC is useful for predicting CRIME rates. Explain. e. Is there statistically significant evidence against the hypothesis that EDUC and CRIME are independent in Florida counties? Explain your reasoning f. Use the value of ? to compute the correlation coefficient. Does this number align with your eye-ball estimate based on the scatter plot? g. Interpret the slope coefficient in the LSQline, CRIME--42.9+1.44 EDUC, in the words of the problem. [Use a reasonable increment in EDUC. If your interpretation sounds causal, do you mean it to? That is, do you think EDUC is causing CRIME to increase?] h. Think of at least one confounding variable that may explain the positive EDUC CRIME relationship.

Answer 1

The regression line is CRIME = -42.9 + 1.44*EDUC

a.

Scatterplet ol CRIME .EDEK 120 100 3 60 20 50556065797560郷 DAE completing high school

b. Given: EDUC = 75.2, Crime = 41.3, we have

CRIMEpred = -42.9 + 1.44*75.2 = 65.39

Residual = Crime - CRIMEpred = 41.3 - 65.39 = -24.09

c. With 20% high school graduation rate

CRIMEpred = -42.9 + 1.44*120 = 129.9

According to the prediction, as the proportion of high school graduate increases CRIME increases which is not appropriate.

d. r² = 0.234 implies that EDUC explains 23.4% variation of variable CRIME.

e. The scatter plot has no perticular trend impling that there might not be any relationship between EDUC and CRIME.

f. Correlation coefficient = $\sqrt{r^{2}}$ = 0.484.

g. According to the regression line the slope implies that with every unit change in EDUC there will be a 1.44 unit change in CRIME. Increase in EDUC will increase the value of CRIME (which does not make sense in real life).