Question

Exhibit 1:  

We have the following information about number of violent crimes (Y) and the number of police personnel (X) for a certain year for a sample of three metropolitan areas. We also know the following statistics: SST = 1250, SSE = 937.5

Crime (Y)	Police Personnel (X)
300	5000
325	3000
350	4000

Question 6

1. To answer this question, refer to Exhibit 1 in question 1.

   What does value of r² tell you?

   A.		25 percent of variation in crime is explained by the number of police personnel.
   B.		50 percent of variation in crime is explained by the number of police personnel.
   C.		75 percent of variation in crime is explained by the number of police personnel.
   D.		None of the above

Question 7

1. To answer this question, refer to Exhibit 1 in question 1.

   The coefficient of correlation is (to 2 decimal places)

   A.		0.87
   B.		-0.87
   C.		0.5
   D.		-0.5

Question 8

1. To answer this question, refer to Exhibit 1 in question 1.

   What is the estimate of the standard error of the overall regression (to 2 decimal places)?

   		10.91
   		30.62
   		45.88
   		55.67

  

Question 9

1. To answer this question, refer to Exhibit 1 in question 1.

   What is the estimate of the standard error of slope estimate (to 3 decimal places)?

   		0.001
   		0.015
   		0.022
   		0.053

Question 10

1. To answer this question, refer to Exhibit 1 in question 1.

   Is police personnel a significant variable affecting crime in the above data?

   		No because we cannot reject the null the slope is 0.
   		Yes because we can reject the null the slope is 0.
   		Need more information to answer the question

Answer 1

We use minitab to solve the problem using following steps :

Stat, regression, regression, fit regression model.

Output :

6) R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression. A value of 100% indicates that the model explains all the variability of the response data around its mean

as shown above, the value of R-sq is 25% so option (a) is correct. i.e 25 percent of variation in crime is explained by the number of police personnel.

7) steps to find correlation coefficient of X and Y :

Stat, basic statistics, correlation.

Hence, option (d) is correct. i.e the coefficient of correlation is - 0.5

8) the estimate of the standard error of the overall regression is 30.6186 ( as given in the above image : value of S under model summary) when corrected upto two decimal place, it is 30.62

So,option (ii) is correct.

9)estimate of the standard error of slope estimateis 0.0217 as shown in the above image (SE coef of police personnel (x)) and when corrected upto 3 decimal place it becomes 0.022

So option (iii) is correct.

10) as p-value =0.667 >0.05, we cannot reject the null hypothesis, the slope is 0. So, option (i) is correct i.e police personnel is not a significant variable affecting crime in the above data.