Question

A set of (x,y) paired data values yields the following results: the x values have a sample mean of 12, the y values have a sample mean of 38, the y values have a sample standard deviation of 4, the x values have a sample standard deviation of 3, and the correlation coefficient between x and y is .76. Compute the least squares regression line for the data, and then predict what the y value should be if x is 4.

Answer 1

Answer:

Least square regression:

y = 1.0136x + 25.8404

Value of y if x is 4:

y = 29.8936

Step-by-step explanation:

Given:

x' = 12

y' = 38

$\sigma y = 4$

$\sigma x = 3$

coefficient between x and y, r = 0.76

Take the least square regression as:

y - y' = byx (x - x')

Let's find byx:

$byx = r (\frac{\sigma y}{\sigma x})$

$byx = 0.76 (\frac{4}{3}) = 1.0133$

We'll now compute the least squares regression line for the data, and then predict what the y value should be if x is 4.

Take the regression equation:

y - y' = byx (x - x')

Substitute figures:

y - 38 = 1.0133 (x - 12)

Expand the equation:

y - 38 = 1.0133x - 12.1596

y = 1.0133x - 12.1596 + 38

y = 1.0136x + 25.8404

The y value when x= 4:

y - 38 = 1.0133(4) + 25.8404

y - 38 = 4.0532 + 25.8404

y = 29.8936

Therefore,

Least square regression:

y = 1.0136x + 25.8404

Value of y if x is 4:

y = 29.8936