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

Answer:

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.)

Step-by-step 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.)