Question

The mean and standard deviation for number of robberies in the U.S. from 2000 to 2015 are x̄ = 354,718 and sx = 28,803. The mean and standard deviation for number of assaults in the U.S. for the same time period are ȳ = 774,140 and sy = 44,910. The correlation coefficient is r = 0.84. Find the equation for the least-squares regression line for number of assaults compared with number of robberies. ŷ = 309,552.15 + 1.31x ŷ = 1.31 + 309,552.15x ŷ = 546,641.84 + 0.64x ŷ = 0.64 + 546,641.84x Unable to determine the equation

Answer 1

Answer:

$\hat{y}=309,552.15 + 1.31x$

Step-by-step explanation:

The equation for the least-squares regression is,

$\hat{y}=a+bx$

where b is the slope and a is the intercept.

They can be found out by,

$b=r\cdot \dfrac{SD_y}{SD_x},\\\\a=\overline{y}-b\overline{x}$

where,

r = correlation coefficient = 0.84

$SD_y$ = standard deviation of y = 44,910

$SD_x$ = standard deviation of x = 28,803

$\overline{y}$ = mean of y = 774,140

$\overline{x}$ = mean of x = 354,718

Putting the values,

$b=0.84\cdot \dfrac{44910}{28803}=1.309\approx 1.31$

$a=774140-(1.31\times 354718)\approx 309,552.15$

Therefore the equation is,

$\hat{y}=309,552.15 + 1.31x$