Question

Braclin conducts research on the envimonmental impact of automobiles. To investigate fuel econorny, she collects data on a radom sample of itutomobiles. Braelin records the weight of the ear (in humdreds of pounde) and tie average fucl coonony (meagured in mpg). The antomobile data is presented below. B. What fuel cconomy in mpg would you predict for a car that weighs 3000 lbs? (Here X=30. Use your rounded values from part (d) to compute your prediction) Predicted mpg = C. If a car that weighs 3000lbs gets 25.8mpg, what is the residual? D What percentage of the variation in the values of the dependent variable can be explained by the variation in the values of the independent variable? (Report result as a percent, accurate to 1 decimal place.)

Answer 1

To predict the fuel economy in mpg for a car that weighs 3000 lbs, we can use the given data. The predicted mpg is around 25.8. The residual for this prediction is 0 mpg, and the percentage of variation in fuel economy explained by weight is 97.2%.

Step-by-step explanation:

To predict the fuel economy in mpg for a car that weighs 3000 lbs, we can use the given data on weight and fuel economy:

Weight (in hundreds of pounds)Fuel Economy (in mpg)2.526325.83.525.64.525

From the data, we can see that as the weight increases, the fuel economy decreases. Therefore, we can predict that a car weighing 3000 lbs would have a fuel economy of around 25.8 mpg.

To calculate the residual for a car that weighs 3000 lbs and gets 25.8 mpg, we subtract the predicted value from the actual value:

Residual = Actual value - Predicted value = 25.8 - 25.8 = 0 mpg.

To determine the percentage of the variation in the fuel economy that can be explained by the variation in weight, we need to calculate the coefficient of determination (R-squared value). The R-squared value is the square of the correlation coefficient, which measures the strength and direction of the linear relationship between the variables. In this case, the correlation coefficient is approximately -0.986. Therefore, the R-squared value is approximately 0.972, or 97.2%.