Question

The mean and standard deviation for number of battery crimes in the U.S. from 1985 to 2000 are X = 326,845 and sx = 27,569. The mean and standard deviation for number of property crimes in the U.S. for the same time period are y = 634,235 and Sy = 42,268. The correlation coefficient is r = 0.92. Find the equation for the least- squares regression line for number of property crimes compared with number of battery crimes.
A: y = 1.41 + 173,214.37x
B: y = 173,214.37 + 1.41x
C: y = 421,052.69 + 0.65x
D: y = 0.65 + 421,052.69x
E: Unable to determine the equation​

Answer 1

Answer:

The correct answer is: A

Step-by-step explanation:

The value of the slope and intercept is:

=0.92(42268/27569)

=1.410518

a=y-bx

=634235-1.410518×326845

=173214.3716

The eququation for the least-square regression line is:

y=173214.3716 + 1.4105518x

Round to the 2 decimal place:

=173,214.37 +1.41x

Answer 2

The equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37

How to determine the least square regression equation?

The given parameters are:

• Mean x, μ = 326,845
• Standard deviation of x, σ = 27,569
• Mean y, μ = 634,235
• Standard deviation of y, σ = 42,268
• Correlation coefficient, r = 0.92

Calculate the slope (m) using:

m = r * Sy/Sx

This gives

m = 0.92 * 42268/27569

Evaluate

m =1.41051761036

Approximate

m = 1.41

The y-intercept (c) is calculated using:

c = μy -m * μx

So, we have:

c = 634235 - 1.41051761036 * 326845

Evaluate

c = 173214.371642

Approximate

c =173214.37

The least-square regression line equation is represented as:

y = mx + c

So, we have:

y = 141x + 173214.37

Hence, the equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37

Read more about least squares regression at:

https://brainly.com/question/14563186

#SPJ2