"Old Vehicles In Exercises 31–34, use the figure shown at the ...

Question

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Table showing the average age of vehicles on U.S. roads from 2014 to 2021, with years and corresponding ages in years.

Error of Estimate Find the standard error of estimate Se and interpret the results."

Accepted Answer

All right, hello, everyone. So, this question says, the table shows the average vehicle age in years for each of the 8 years. A regression model has been fit to the data shown here. Using this regression model and the actual data computed the standard error of estimate as sub. S E which measures the typical distance between observed and predicted values. Here we have 4 different answer choices labeled A through D. All right, so first, let's recall the formula for SE to have as a reference. S E Is equal to the square root of. The sum of all square differences between. Observed and expected values. Divided by and subtracted by 2. Keep in mind that in the formula here, Y1 represents the observed value listed here in the data table, whereas Y hat sub1 represents the expected value calculated from the regression model. So here, we're already given the regression model. Which means that to find Y hat for each data point, you would simply plug in each vehicle age in years. Into your formula as the X value. So once you do this, you would then subtract the difference between each observed value and each expected value calculated from the regression model. And then after you do this, you would then calculate. The square Of the difference calculated previously. And so for the calculation of a sub E, It is the value of those squared differences that you're going to need to find the sum of. Ultimately, the sum of all squared differences. is equal to 0.01406. So now going back to your formula. S E is equal to the square root of 0.01406. Divided by And subtracted by 2, which gives you 6. And this ultimately equals approximately 0.0484. Ultimately, the standard error of estimate is approximately 0.0484 years, corresponding to option D in the multiple choice. This means that the predicted values differ from the actual values by about 0.05 years on average. This is also suggesting that the regression line is a good fit for the data. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Error of Estimate Find the standard error of estimate Se and interpret the results."

Key Concepts

Standard Error of Estimate (Se)

Regression Analysis

Interpretation of Results

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