Compute the least-squares regression line for predicting
from x and y given the following summary statistics. Round the slope and y-intercept to at least four decimal places.
x̄ = 3
sx = 22000
ȳ = 102
sy = 15
r = .40
Is this correct: 93.8182 + 2.7273x ?
To compute the least-squares regression line, we can use the following formula:
b = r * (sy / sx)
Where b is the slope of the regression line, r is the correlation coefficient, sy is the standard deviation of the y values, and sx is the standard deviation of the x values.
In this case, the given summary statistics are:
x̄ = 3 (mean of x values)
sx = 22000 (standard deviation of x values)
ȳ = 102 (mean of y values)
sy = 15 (standard deviation of y values)
r = 0.40 (correlation coefficient)
First, calculate the slope (b) using the formula:
b = r * (sy / sx)
b = 0.40 * (15 / 22000)
Now, let's plug in the values and calculate b:
b = 0.40 * 0.00068
b ≈ 0.000272
The slope (b) is approximately 0.000272.
Next, we can calculate the y-intercept (a) using the formula:
a = ȳ - (b * x̄)
a = 102 - (0.000272 * 3)
Now, let's plug in the values and calculate a:
a = 102 - 0.000816
a ≈ 101.999184
The y-intercept (a) is approximately 101.999184.
Therefore, the least-squares regression line for predicting y from x is:
y ≈ 101.9992 + 0.0003x
Based on this calculation, the correct regression line is actually 101.9992 + 0.0003x.