Question

The table displays data for Nutrition Guides of a single serving of particular foods. Assuming there exists a correlation between Calories and Fat Grams, find a linear regression model that determines approximate Fat Grams (y) as a function of Calories (x).

y=0.056x - 1.759


y=0.054x - 2.105


y=14.211x + 68.070


y=13.019x + 85.966

Answer 1

The linear regression model that will determine approximate Fat Grams (y) as a function of Calories (x) is given by

y = 0.054 x - 2.105

Hence the correct option is B.)

Explanation:

Step 1: Find X⋅Y and as it was done in the table below.

Step 2: Find the sum of every column:

ΣX = 1560, ΣY = 67, ΣX.Y = 14860 , ∑(
`\textbf{X}^(2)`) = 337600

Step 3: Use the following equations to find a and b:

a = = -2.105

b =
`\frac{n.\sum{XY} - \sum{X}.\sum{Y}}{n.\sum{(X^(2))}- (\sum{X})^(2) }` = 0.054

Step 4: Substitute a and b in regression equation formula

y = a + b⋅x= −2.105 + 0.054⋅x

The linear regression model that will determine approximate Fat Grams (y) as a function of Calories (x) is given by

y = 0.054 x - 2.105

Hence the correct option is B.)