Question

The table shows the fat content and calories for the burgers at a fast food chain.

Fat (g) 25 44 63 32 37 20 11 52
Calories 590 830 1080 680 750 420 310 820


Write the best fit line that models the impact of fat content on calories. Explain how you got your answer.

Answer 1

We fit a least-squares line y = a + bx with x = fat (g) and y = calories.

Compute sums from the 8 data points:
- n = 8
- Σx = 284
- Σy = 5480
- Σx^2 = 12148
- Σxy = 223270

Slope b = [nΣxy − (Σx)(Σy)] / [nΣx^2 − (Σx)^2]
= [8(223270) − 284(5480)] / [8(12148) − 284^2]
= (1,786,160 − 1,556,320) / (97,184 − 80,656)
= 229,840 / 16,528 ≈ 13.906.

Intercept a = (Σy − bΣx)/n
= (5480 − 13.906·284)/8 ≈ 191.33.

Best-fit line (rounded):
Calories ≈ 191.33 + 13.91·(fat in g).

Interpretation: each extra gram of fat adds about 13.9 calories; a burger with 40 g fat is predicted to have ≈ 191.33 + 13.91·40 ≈ 748 calories.