Question

A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Let the temperature be the explanatory variable and gas consumption the response variable. Assume that the relationship between these two variables is linear. The least-squares regression line for predicting gas consumption from the outside temperature is:

Consumption = 1360 - 20*Temperature

1. In the equation, gas consumption is the response (dependent or predicted) variable. Explain why it makes sense for gas consumption to be the response (dependent or predicted) variable in this situation.

2. Identify and interpret the slope of the regression line in context.

3. Identify the intercept of the regression line. If appropriate, interpret the y-intercept in context. If not, explain why it is not appropriate to interpret the intercept in this situation.

4. Predict the gas consumption for a day that is 10 F outside.

Answer 1

Consumption = 1360 - 20*Temperature

(1) In this case, it makes sense to use gas consumption as a dependent variable on the temperature because we can think of changing the gas consumption based on change in temperature, but we can never think of finding a change in temperature due to change in gas consumption. So, it makes sense to use gas consumption as a dependent variable

(2) Slope coefficient is -20, which indicates that for one degree fahrenheit increase in temperature, the gas consumption will decrease by 20 cubic feet per day.

(3) Intercept coefficient is 1360, which indicates that when temperature is 0 degree, the gas consumption will be maximum, i.e. 1360 cubic feet per day

(4) set temperature = 10, we get

Consumption = 1360 - 20*10

= 1360-200

= 1160cubic feet per day