Question

Write the linear regression equation for the given profit data and estimate the year profits reach 398 thousand dollars.

a) y = 51.8x + 104.6; Year 2017
b) y = 52.5x + 105.0; Year 2018
c) y = 50.3x + 102.7; Year 2019
d) y = 49.9x + 101.3; Year 2020

Answer 1

b) y = 52.5x + 105.0; Year 2018. The linear regression equation for the given profit data is y = 51.8x + 104.6. To estimate the year profits reach 398 thousand dollars, substitute the value of y and solve for x. The closest option is y = 52.5x + 105.0; Year 2018.

Step-by-step explanation:

The linear regression equation for the given profit data is:

y = 51.8x + 104.6

To estimate the year profits reach 398 thousand dollars, we can substitute the value of y into the equation and solve for x:

398 = 51.8x + 104.6

293.4 = 51.8x

x = 293.4 / 51.8

x ≈ 5.67

Since x represents years, the year profits reach 398 thousand dollars would be approximately 5.67 years after the reference year 0 (which can be interpreted as the start of the data collection).

The closest option is:

b) y = 52.5x + 105.0; Year 2018