Question

The data below show the number of registered automatic​ weapons, in​ thousands, and the murder​ rate, in murders per​ 100,000, for eight randomly selected states. a. Determine the correlation coefficient between the number of automatic weapons and the murder rate. b. Find the equation of the regression line. c. Approximately what murder rate can we anticipate in a state that has 13 thousand registered​ weapons? Automatic weapons comma x 11.5 8.2 6.8 3.3 2.6 2.7 2.2 0.3 Murder rate comma y 13.1 10.6 11.2 10.6 5.5 6.2 3.3 4.8 a. Determine the correlation coefficient. requals nothing ​(Do not round until the final answer. Then round to two decimal places as​ needed.) b. Find the equation of the regression​ line, yequals mxplus b. First find the​ slope, m. mequals nothing ​(Round to two decimal places as​ needed.) Now calculate the​ y-intercept, b, of the regression line. bequals nothing ​(Round to two decimal places as​ needed.) c. Approximate the murder rate in a state that has 13 thousand registered weapons. yalmost equals nothing murders per​ 100,000 ​(Round to one decimal place as​ needed.)

Answer 1

Answer

(A) copy and paste the data in excel sheet

use CORREL function in excel to find the correlation coefficient

select x values as array 1 and y values as array 2

we get

r = CORREL(x,y)

= 0.86

(B) Using TI 84 calculator

enter the data x values in list L1 and y values in list L2

press stat then calc then LinReg(ax+b)

select data set L1 as X list and L2 as Y list

press calculate

we get

slope (m) = 0.82

and intercept (b) = 4.29

Regression equation is y = 0.82x + 4.29

(C) setting x = 13

we get

y = 0.82*13 + 4.29

= 15.0