M 670 Exam I Spring 2016 Name: Cynthia Sockwell This exam is worth 75 points (2 are free). Point values for each problem are in parentheses. 1. See the plots on the next page labeled a, b, and c. For each, describe the relationship present in the scatterplot. (3 ea.) a. Weak positive nonlinear relationship b. No relationship c. Strong positive linear relationship 2. In plot a, we are looking at the relationship between a worker's score on a dexterity test and his or her corresponding number of units produced. Suppose a new applicant scored 8 on the dexterity test. Would you expect a regression model based on this data to accurately predict this applicant's production? Explain. (3) I do not think that a regression model would accurately predict the applicant's production because it is a nonlinear relationship. The graph of these plots is slightly curved rather than a straight line. Each dexterity score (y) will not predict the number of units produced (x). As the score increases the units produced can either increase or decrease. There are other factors that should be considered when determining the number of units produced by applicants and employees. 3. In plot b, we are predicting employee salaries using the number of years of higher education completed. Is the relationship present in the plot surprising? Also, briefly discuss a possible explanation for the relationship. (4) No the non existing relationship between number of years of higher education and salary is not surprising. A possible explanation for the two variables not having a relationship could be because of experience. There are some people that may not have as high of an education as others, but they have more experience in the field and know the job in and out. That could qualify them for higher pay. Another reason that could possibly have this effect is the specific job. Some people may go to school for their bachelors, masters, etc, but they get a job that is irrelevant to their degrees so they are not getting paid for the knowledge they have learn. There are endless amounts of reasons this could happen. 4. Refer to plot c and the seasonal exponential data for Sally's Stenography Source. a. What type of model appropriate for the data? Explain. (3) The appropriate model for the data would be simple linear regression because there is a linear relationship between the one independent variable of the quarter and the one dependent variable of the sales. b. Use that model, and discuss its efficacy. (How well does it perform?) (4) When you plug in the data into excel and run a regression model you get an R = 0.9568, an R-squared = 92% and a P value of 4.0638E-15. These results show that there is a strong linear relationship between the quarter and the amount of sales in dollars for Sally. There is a good line of fit and this data is statistically significant. That would mean you reject the null because as the quarters progress the sales increase. c. Offer any suggestions to improve the model performance. (3) A good way to improve the model of performance with this data would be to 5. The table below features three exponential smoothing models used on the same set of data. Type MSE Model 1 Exponential Smoothing 8755.3 Model 2 Trend 4876.2 Model 3 Trend with Seasonality 5945.8 a. Based solely on the information in this output, what would you conclude about the underlying data set? Explain. (3) b. Are there any other possible explanations for the values in the table? Explain. (3) For 6-12, refer to the attached regression output. Here we are using years of experience, college GPA, and company entrance score to predict employee salaries at a local firm. 6. We would conclude that the overall model (using all three explanatory variables) is statistically significant at the .05 level. (2) false 7. None of the explanatory variables are useful predictors. (2) a. false 8. The most useful predictor in the presence of the other explanatory variables is company entrance score. (2) 9. Multicollinearity is (3) Severe. 10. Which of the following combinations would be expected to yield the highest pay? Values are years, GPA, and score. (2) 8, 3.6, 85 11. Interpret the coefficient of determination for the overall (3-variable) model. (3) The overall model has an R-squared of 0.471 or 47%. This low percentage tells us that 47% of the variability of salaries can be explained by experience, GPA, and entrance score. This leaves a large percentage of 53% (over half) that is unexplained. There is a strong positive linear association between the variables, but it is not strong enough to accurately predict someone's salary level. 12. The model in Summary Output 2 uses only entrance score to predict salary. a. Write the least squares regression equation. (2) y = 8.10 + 0.84 x b. Is this a useful model? Explain. (3) No this is not a useful model. It could go either way. There is not a good line of fit, there is a weak positive correlation, and there is a low percentage of explanation to employees' salaries and their entrance score. There is a useful linear association between the two, but I feel like this could not be the determinant factor of an employee's salary. There would need to be more information. c. Is the output consistent with the other output? Explain. (3) 13. Given the information, which answer is BEST? (4) X-variables R2 Adjusted R2 MSE Model 1 6 .9344 .9058 5867.53 Model 2 4 .9277 .9133 5746.09 Model 3 3 .8761 .8497 5844.78 We would most likely prefer Model 2. 14. Refer again to the Sally's Stenographer data. Use exponential smoothing with a smoothing constant = 0.2. This model (4) Tends to under predict 15. In the previous problem, suppose we used a different smoothing constant value. This change would (4) Possibly generate a better model (with respect to prediction) 16. You are tracking mall sales over a two-year period. (2) The data will surely contain a trend component. 17. In #16, suppose we track sales over a one-year period. (2) The data will likely contain a verifiable seasonal component. 18. Discuss how a method on this exam can be used to catch data errors such as data entry mistakes. (3)