Question

Rose drew a regression line for this paired data set. Her line passed through (1, 2) and (3, 5). What is the equation of Rose's regression line? Responses yˆ=6.8x+1.6 y hat equals 6.8 x plus 1.6 yˆ=1.5x+0.5 y hat equals 1.5 x plus 0.5 yˆ=0.66x−0.33 y hat equals 0.66 x plus 0.33 yˆ=2x+1 y hat equals 2 x plus 1

Answer 1

Answer: The equation of a line in the form of y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the slope, you can use the two points on the line: (1, 2) and (3, 5). The slope is found by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

m = (5 - 2) / (3 - 1) = 3 / 2 = 1.5

The y-intercept can be found by plugging in one of the points and the slope into the equation and solving for b. Let's use the point (1, 2).

2 = 1.5 * 1 + b

b = 2 - 1.5 = 0.5

So the equation of the regression line is:

y = 1.5x + 0.5

Therefore, the correct answer is: yˆ = 1.5x + 0.5

Explanation: