Question

The table shows the age of a painting (x) in years, and its estimated dollar value (y). Which regression equation correctly models the data?

A. y = 41.47x + 0.09
B. y = 41.47x + 1.27
C. y = 153.32x - 688.54
D. y = 153.32x - 6.32

Answer 1

The correct regression equation to model the data is y = 41.47x + 1.27 (option B).

Step-by-step explanation:

The correct regression equation to model the data is y = 41.47x + 1.27 (option B).

To determine the regression equation, we need to find the slope (m) and y-intercept (b). We can use the given data points to calculate the slope using the formula: m = (y2 - y1) / (x2 - x1).

Using the data points (1985, 25.52) and (1990, 34.275), the slope (m) is (34.275 - 25.52) / (1990 - 1985) = 1.755. The y-intercept (b) can be found by substituting the slope and a data point into the equation: y = mx + b. Using (1985, 25.52), we can solve for b: 25.52 = (1.755)(1985) + b. Solving for b, we get b ≈ 1.27.