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

ŷ = 309,459.42 + 1.31x

Explanation:

I took the quiz and got it right

Answer 2

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

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 (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 (44910)/(28803)=1.309\approx 1.31`

`a=774140-(1.31* 354718)\approx 309,552.15`

Therefore the equation is,

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