STAT102Q2_Solutions.pdf - Spring 2017 STAT 102 Quiz 2...

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Spring 2017 STAT 102 Quiz 2 Solutions February 27, 2017 Question 1. A database IT team ran a simple linear regression of “result time” (in sec- onds) against “query complexity” in order to understand the relationship between these two variables. Results from the regression analysis follow. Which of the following provides the best description of the relationship between the two variables: result time and query complexity? A. There appears to be a positive correlation but it is not statistically significant as suggested by the small R 2 value. B. The result time is expected to increase by 0.074 seconds per unit increase in query complexity. C. The sample correlation coefficient between the two variables is equal to 0 . 066. D. There is statistically significant evidence that the slope of the true regression line is different from zero. Solution : The answer is D. A is incorrect because the R 2 value does not have any associated p -value reported in the question, and so we cannot judge whether the positive correlation is significant or not based on it. B is incorrect because 0.074 is the estimated standard error of b 1 rather than b 1 itself. C is incorrect and the sample correlation coefficient here is 0 . 066 = 0 . 257. D is correct because the associated p -value for testing H 0 : β 1 = 0 against a two-sided alternative is 0.0002 which is smaller than 0.05.
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