Question

Linear Regression Application, Interpolation and Extrapolation Use the data and story to answer the following questions The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. * 11.6 14.2 8.1 11.2 7.2 10.2 3.9 2.9 7.1 6.7 2.3 6.1 2.5 6.2 0.5 4.2 x = thousands of automatic weapons y = murders per 100,000 residents Use your calculator to determine the equation of the regression line. (Round to 2 decimal places) Determine the regression equation in y = ax + b form and write it below. Preview A) How many murders per 100,000 residents can be expected in a state with 6 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 8.2 thousand automatic weapons? Answer = Round to 3 decimal places.

Answer 1

Solution:

The independent variable is 2, and the dependent variable is y. In order to compute the regression coefficients, the following table needs to be used: 164.72 201.64 125.44 104.04 50.41 10.2 90.72 73.44 27.69 19.43 14.03 15.5 21 134.56 65.61 51.84 15.21 8.41 5.29 6.25 0.25 287.42 44.99 6.1 6.2 4.2 37.21 38.44 0.5 17.64 Sum= 407.63 619.71 Based on the above table, the following is calculated: S = ; = * = 4.175 8 = x = 450 =52875 88xx = x + ( x ) = 287.42 – 302 /8 = 97.295 Sbuy = - - (Šx) = 619.71 – 65.8/8 = 768875 55x = 9x2 + () (2x) – 407 .63 – 30 x 65.978 = 86.3675 SSXY =) = 407.63 - 39 x 65.9/8 = 86.3675 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows: SSXy86.3675 SSXX - 97995 = 0.8877 n=Y -Xm= 8.2375 - 4.875 x 0.8877 = 3.91 Therefore, we find that the regression equation is: y = 3.91 +0.88777

A) Regression equation y = 3.91+0.8877x
x = 6
y = 3.91+0.8877(6) = 9.236

B) Regression equation y = 3.91+0.8877x
x = 8.2
y = 3.91+0.8877(8.2) = 11.189