What can we say about the regression model?

a. The model explains 17.12% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs.
b. The model explains 27.78% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 19.28% of the sample variability of heating costs.
c. The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 17.12% of the sample variability of heating costs.
d. The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs.

b. The model explains 27.78% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 19.28% of the sample variability of heating costs.

Step-by-step explanation:

Hello!

One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1) and the amount of insulation in inches (X2). Given below is the EXCEL output of the regression model.

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables. Each time you add another explanatory variable to the regression the coefficient increases regarding of real contribution of the new variable. This could lead to thinking (wrongly) that the new variables are good to explain the dependent variable.

The adjusted coefficient of determination is a correction made to the raw coefficient of determination to have a more unbiased estimation of the effect the independent variables have over the dependent variable.

In the regression output, the R² is 27.78% and the corrected R² is 19.28%

The correct interpretation of these two values is:

b. The model explains 27.78% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 19.28% of the sample variability of heating costs.

I hope it helps!

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²