Sal recorded the cost of his monthly home heating bill and the corresponding average monthly temperature for the past 15 months. He displayed the information in a scatter plot and used a graphing calculator program to find the least squares regression line to fit the data. Sal wants to use the least squares regression line to predict the cost of his heating bill when the average monthly temperature is 40°F. Which statement is true

Question

Sal recorded the cost of his monthly home heating bill and the corresponding average monthly temperature for the past 15 months. He displayed the information in a scatter plot and used a graphing calculator program to find the least squares regression line to fit the data. Sal wants to use the least squares regression line to predict the cost of his heating bill when the average monthly temperature is 40°F. Which statement is true?

The heating bill will be exactly $95.28 for an average monthly temperature of 40°F.
The heating bill will be about $95 for an average monthly temperature of 40°F.
Sal cannot use this line to make predictions because it does not fit the data well.
Sal cannot use this line to make predictions because there is no data for an average monthly temperature of 40°F.

Quizzma Team · Answer

The correct statement is: The heating bill will be about $95 for an average monthly temperature of 40°F. Explanation: In least squares regression, the line generated is used to estimate or predict values based on the existing data. When Sal inputs the temperature of 40°F into the regression equation, it will yield an approximate predicted value for the heating bill. While it won’t be exact, it will provide a reasonable estimate based on the trend established by the previous data. The other options either imply a certainty that isn’t inherent in predictions or suggest limitations that don’t apply as long as the regression model is well-fitted.

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