Question

The correlation coefficient between time studied and points earned on a midterm is 0.8. If the mean study time was 180 minutes with a standard deviation of 16 minutes, and the mean score on the test was 75 points with a standard deviation of 8 percentage points, find the equation of the least squares regression line.

a. y = 0.8x + 60
b. y = 10x + 60
c. y = 0.5x + 80
d. y = 1.5x + 70

Answer 1

The equation of the least squares regression line can be found using the formula y = a + bx, where y is the dependent variable, x is the independent variable, b is the slope, and a is the y-intercept.

Step-by-step explanation:

The equation of the least squares regression line can be found using the formula:

y = a + bx

where y is the dependent variable (points earned), x is the independent variable (time studied), b is the slope of the line, and a is the y-intercept.

1. First, calculate the slope (b) using the correlation coefficient (r) and the standard deviations of both variables: b = r * (standard deviation of y / standard deviation of x)
2. Next, calculate the y-intercept (a) using the mean values of both variables: a = mean of y - b * (mean of x)
3. Substitute the values of a and b into the equation to obtain the equation of the least squares regression line.

Based on the given information, the equation of the least squares regression line is y = 0.8x + 60. Therefore, the correct answer is option a. y = 0.8x + 60.