"In Exercises 17 and 18, use the data to (a) find the coeffici...

Question

"In Exercises 17 and 18, use the data to (a) find the coefficient of determination r^2 and interpret

the result, and (b) find the standard error of estimate s_e and interpret the result.

17. The table shows the times (in seconds) to accelerate from 0 to 60 miles per hour and the top speeds (in miles per hour) for eight electric cars. The regression equation is y =- 14.399x + 196.996. (Source: Car and Driver)

Table displaying acceleration times and top speeds for eight electric cars, with data for analysis.

Accepted Answer

All right, hello, everyone. So, this question says, a researcher is studying the relationship between the number of hours employees spend in professional training sessions per month, X, and their job performance ratings, Y, scored out of 100. A linear regression model is created to predict job performance based on training hours, and the resulting regression equation is Y hat equals 2.8X added to 65. The researcher collects data from a sample of 10 employees. Based on this data, the residual sum of squares SSR is equal to 82.4. And the total sum of squares SST is equal to 240. What is the coefficient of determination are squared and what does it tell us about the model? Here we have 4 different answer choices labeled A through D. All right, so first, let's begin with finding R squared. And recall that R squad, the coefficient of determination, is equal to 1 subtracted by SSR divided by SST. So, plugging in the information that we provided, R squared is equal to one subtracted by. 82.4 Divided by 240. So this expression then simplifies to one subtracted by 0.3433. Which gives you a value for R squared. Equal to 0.6567. So, what does the the coefficient of determination actually tell you? Well, recall that the coefficient of determination, when converted into a percentage, is the percentage of variability. That's explained by the regression model. So applying that definition into the context of this experiment. The coefficient of determination means that there is. Or rather that approximately 65.7% of the variability in job performance can be explained by the number of hours spent in professional training. This suggests a moderately strong positive linear relationship between training hours and job performance. So, essentially, as they dedicate more time to completing these trainings, their ratings will go up in a predictable manner, generally. So ultimately Our correct answer is going to be option C in the multiple choice, which reads R squared is equal to 0.657, 65.7% of the variation in job performance is explained by training hours. And so with that being said, thank you so very much for watching, and I hope you found this helpful.

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