. Question 2 Here is a bivariate data set. X y 62 75 52 B2 64 24 67 8 81 14 68 24 54 78 79 -18 66 76 71 72 Find the correlation coefficient and report it accurate to four decimal places. Submit Question. Question 9 The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states 11.6 8.1 6.9 3.6 2.7 2.7 2.7 0.6 y 13.6 10.9 10.2 7.3 6.5 6.5 |6.6 4.5 r = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation y = 0.821 + 4.28. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 6.6 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 2.2 thousand automatic weapons? Answer = Round to 3 decimal places. Submit QuestionQuestion 11 Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant positive linear correlation between advertising cost and profit . Use a significance level of 0.05 and round all values to 4 decimal places. Advertising Cost | Profit 3 19 29 22 18 27 8 27 Ho: p = 0 Ha: p > 0 Find the Linear Correlation Coefficient Find the p-value p-value = The p-value is O Less than (or equal to) a O Greater than a The p-value leads to a decision to O Accept Ho O Do Not Reject Ho O Reject Ho The conclusion is O There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit O There is a significant positive linear correlation between advertising expense and profit. There is a significant linear correlation between advertising expense and profit. O There is a significant negative linear correlation between advertising expense and profit.O Question 12 A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Lovers 7 7 7 5 7 7 8 GPA 2.7 2.1 2.7 2 2.7 2.2 2.1 1.7 a. Find the correlation coefficient: T = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: 2v = 0 # 0 The p-value is: (Round to four decimal places) c. Use a level of significance of o = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful. There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. d. p' = (Round to two decimal places) e. Interpret p2 : O There is a 65% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had O 65% of all students will have the average GPA. O There is a large variation in students' GPAs, but if you only look at students who have had a fixed number of lovers, this variation on average is reduced by 65%. O Given any group of students who have all had the same number of lovers, 65% of all of these studetns will have the predicted GPA. f. The equation of the linear regression line is: y = I (Please show your answers to two decimal places) g. Use the model to predict the GPA of a college student who as had 8 lovers. GPA = (Please round your answer to one decimal place.) h. Interpret the slope of the regression line in the context of the question: O The slope has no practical meaning since a GPA cannot be negative. O As x goes up, y goes down. O For every additional lover students have, their GPA tends to decrease by 0.29. i. Interpret the y-intercept in the context of the question: The average GPA for all students is predicted to be 4. 19. The best prediction for the GPA of a student who has never had a lover is 4.19. Olf a student has never had a lover, then that student's GPA will be 4. 19. The y-intercept has no practical meaning for this study