UF MAR 5621 - Correlation and Simple Regression practice problems

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Practice Problems on Correlation & Simple Regression1. Suppose that, across a sample of stores, the correlation coefficient between beer prices and beersales is -0.65. What does this number indicate?(a) There is almost no variability in beer sales that is unexplained by beer price. (b) More beer sales tend to go along with lower beer prices. (c) As price increases by $1, beer sales decrease by 65%(d) All of the above are true.2. The purpose of a scatterplot is: (a) To test for the significance of association in bivariate data. (b) To calculate the correlation coefficient. (c) To provide a visual picture of the relationship in bivariate data. (d) To determine a confidence interval for the regression slope. 3. The standard error of the sample regression slope tells you: (a) Approximately how different the slope coefficient will be in different samples.(b) Approximately how large the prediction errors are. (c) Approximately how spread out the Y scores are. (d) Approximately how much of the variability of Y is explained by X. 4. The correlation coefficient describes the _________ between 2 variables.(a) strength of curved association(b) strength of random association(c) strength of linear association(d) American Marketing Association5. R2 is a measure used to describe the overall fit of the regression line. Which of the following statements is/are correct about R2?(a) In general, the closer the R2 is to 1, the better the fit of the regression line to the points in the scatterplot.(b) R2 tells you the proportion of the points in the scatterplot that fall right on the regression line.(c) R2 will always decrease as you add new observations to your regression.(d) All of the above are true statements about R2.6. A cost accountant is developing a regression model to predict the total cost of producing a batch of circuit boards as a function of the batch size. The independent and dependent variables for this regression would be:(a) IV: circuit board DV: batch size(b) IV: batch size DV: total cost(c) IV: average cost DV: circuit board(d) IV: total cost DV: average cost(The next 9 questions are based on the following information.)Pete Estrian is looking to buy a used Honda Civic. He checks the Internet and finds a huge list ofCivics for sale in his area. He selects a random sample of 10 cars, ranging in age from 2 years old to 15 years old. For each car, he enters the age (in years) and the offered sales price (in thousands) into Excel. He runs a regression predicting price from age, and gets the following (edited) output:ANOVA df SS MS F Significance FRegression 1 93.5 93.51 117.0 0.000005 Residual 8 6.4 0.80Total 9 99.9 Coefficients Standard Error t Stat P-value Intercept 12.10 0.60 20.2 0.00000004 Age -0.80 0.07 -10.8 0.000005 7. What is the equation for the regression line?(a) Predicted price = $12,100 - $800 * Age(b) Predicted price = $12,100 - $600 * Age(c) Predicted price = $20,200 - $10,800 * Age(d) Predicted price = $12,100 - $70 * Age8. Car #5 in the sample was 10 years old and cost $4,000. Determine the predicted price and the residual for this car.(a) Predicted price = $11,300; residual = -$7,300(b) Predicted price = $11,300; residual = $7,300(c) Predicted price = $4,100; residual = $100(d) Predicted price = $4,100; residual = -$1009. Construct a 95% confidence interval for the drop in price associated with an additional year of age.(a) ($639, $961)(b) ($667, $933)(c) ($749, $851)(d) Cannot be determined from the information given10. What is the correlation between Age and Price?(a) r= 0.97(b) r= -0.97(c) r= 0.80(d) r= -0.80(Honda Civics Prices and Ages, continued.)11. What is the typical difference between the predicted prices (based on the regression line) and the actual prices for these cars? (a) about $70(b) about $600(c) about $890(d) about $2,53012. What does the p-value of 0.000005 tell us?(a) It is not very plausible that the population regression line relating Price to Age is flat.(b) There is strong evidence that the slope of the population regression line is not 0.(c) There is strong evidence that the knowing a Civic’s age would improves our prediction of itsprice. (d) All of the statements above are implied by the low p-value.13. The average age of the cars in the sample is 7.1 years. What is the average price of the cars inthe sample?(a) $5,000(b) $6,420(c) $7,190(d) Cannot be determined from the information given.14. What is the best conclusion we can draw about Honda Civics that are 5 years old, based on the information we have?(a) We conclude that the average price of 5-year old Civics is about $8,100, but we expect to seesome differences in prices for different 5-year Civics.(b) We conclude that that all 5-year-old Civics should cost the same, about $8,100.(c) We conclude that all 5-year-old Civics should cost more than all 6-year-old Civics, although we can’t be completely sure by how much.(d) All of the above are equally valid conclusions.15. Suppose instead that Pete had taken a second sample, consisting of 6 cars that ranged in age from 4 to 8 years old, and suppose that he regressed Price on Age for this second sample. How would the standard error of the regression slope be different for this second sample (compared to the first sample described on the previous page)?(a) The standard error of the regression slope would probably be larger for the second sample.(b) The standard error of the regression slope would probably be about the same for both samples.(c) The standard error of the regression slope would probably be smaller for the second sample.(The next 5 questions deal with the following information.)Below is partial output from a regression predicting consumption of beef (called BeefConsumption, and measured in pounds of beef per person annually) from the price of beef (called BeefPrice, and measured in cents per pound). [The data are from the United States from 1925 to 1941. During this period, the price of beef ranged from about 55 to 80 cents per pound.]ANOVA df SS MS F Significance FRegression 1 166.0 166.0 19.6 0.0005Residual 15 127.2 8.5Total 16 293.1 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 85.24 7.30 11.67 6.3E-09 69.68 100.80BeefPrice -0.47 0.11 -4.42 0.0005 -0.69 -0.2416. In 1941, beef cost 56 cents per pound, and annual consumption of beef was 60.0 pounds per person. Determine the predicted consumption of beef in 1941, and say whether the data point for 1941 is


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UF MAR 5621 - Correlation and Simple Regression practice problems

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