Question

1. A producer of infant formula wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities: r = 0.9  
= 2.5   = 8       = 1.2   = 3.6
a. Calculate the regression equation for the above information

b. What does this regression equation imply? Specifically explain the meaning of the y-intercept and the slope coefficient.

c. Calculate r2. And put your r2 into the correct statement below.

I.   __________ of the variation in age is explained by weight variation
or
II.   __________ of the variation in weight is explained by age variation.

Answer 1

a)

It is given that the age X (in months) is taken as the explanatory variable and  the average weight Y (in kilograms) is taken as the response variable.

And

r = 0.9

The formula for finding slope is,

So,

The formula for finding intercept is,

So,

Now, the regression equation is,

b)

The slope is 2.7. The slope means that for every one unit increase of age we expect that on average the weight of the children will increase by 2.7.

The y-intercept has no real meaning.

c)

Here

r = 0.9

Coefficient of determination (r2) = (0.9)2 = 0.81

The coefficient of determination (R² or r-squared) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable. In other words, the coefficient of determination tells one how well the data fits the model.

II. 81% of the variation in weight is explained by age variation.