probs-simplereg1-sols - Practice Problems on Correlation...

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1. Suppose that, across a sample of stores, the correlation coefficient between beer prices and beer sales 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. Answer: (b) The correlation is negative, so (b) is correct: higher sales go with lower prices (basic economics also tells us this!) Option (a) is false because while .65 2 = 42% of the variability in sales is explained by price, the remainder (58%) is not explained by price. (we’ll discuss this interpretation of the squared correlation next week) Option (c) is a kind of distorted interpretation of the regression slope , not the correlation coefficient. 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. Answer: (c) The scatterplot is a visual display of bivariate data 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. Answer: (a) The standard error of any quantity is a measure of how different that quantity will be in different samples. So (a) is the correct interpretation of the standard error of the sample regression slope. 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 Association Answer: (c) The correlation coefficient measures linear (straight-line) association: how close the points in a scatterplot fall to a straight line.
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5. R 2 is a measure used to describe the overall fit of the regression line. Which of the following statements is/are correct about R 2 ? (a) In general, the closer the R 2 is to 1, the better the fit of the regression line to the points in the scatterplot. (b) R 2 tells you the proportion of the points in the scatterplot that fall right on the regression line. (c) R 2 will always decrease as you add new observations to your regression. (d) All of the above are true statements about R 2 . Answer: (a) Larger R 2 means a closer fit between the points and the regression line, so (a) is correct Option (b) is not true (for example, because R 2 could be large even if no points fall right on the regression line (so long as most of the points are close to the line) Option (c) is also not true: there is no consistent relation between R 2 and the number of
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probs-simplereg1-sols - Practice Problems on Correlation...

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