Name________________________________ PSU ID_____________________________ STAT 100 Lesson 8 Assignment Answer the following questions and submit for grading. Each question or part of a question is...

Name________________________________ PSU ID_____________________________ STAT 100 Lesson 8 Assignment Answer the following questions and submit for grading. Each question or part of a question is worth 1 point except: 2 is worth 3 points; 3A, 3B, 7A, & 8 are 2 points. 1. For each pair of variables, is the association likely to be a positive association, a negative association, or no association? Explain your reasoning. a. House size in square feet and cost of house ($) b. Outside temperature and amount of oil consumed to heat a home c. Amount of caffeine consumed and GPA 2. In scrambled order, the correlation values for the three scatterplots are -.92, .98, -.26. Match these correlations to the scatterplots found below. 3. A regression equation that describes the relationship between the time spent writing a paper (y) in hours and length of paper (x) in pages is found below. The regression equation of the line is: Time = -1.3 + 1.2 Length a. Interpret the slope in terms of how time spent writing a paper changes as length of paper increases. Be specific. b. Does the y-intercept have a logical interpretation in the context of this problem? (Hint: use Figure A.4 (located below 3f) to help make this decision.) Explain. c. Use the regression plot found below (Figure A.4) to predict approximately how long it would take to finish a paper that is 10 pages in length. Do not use the equation. d. Should the regression equation be used to predict how long it would take to complete a paper that is 40 pages in length? Explain. e. The correlation between the two variables is .917 with a p-value of .0004. What conclusion can be made about the relationship between length of paper and amount of time it takes to complete a paper? f. Suppose the point (x, y) = (25 pages, 35 hours) was removed from the regression plot found below. Would the correlation stay the same, increase, or decrease? Explain. 4. Suppose the correlation found between actual height and ideal height, where both variables are measured in inches, was .45. Can you determine what the correlation would be if actual height and ideal height were converted to centimeters? Explain. 5. Which implies a strong linear relationship, a correlation of +.3 or a correlation of -.7? Explain. 6. Identify the blunder in each of the following statements. a. The correlation between the color of a person's left eye and right eye is 0.99. b. The rankings for college football teams by the Coaches Poll and the AP Media Poll have a correlation of 1.17. c. A study shows that there is a positive correlation between reading ability and shoe size for children between the ages 6 to 10 years. This result shows that an increase in shoe size is responsible for an increase in reading ability. 7. A group of adults aged 20 to 80 years was tested to see how far away they could first hear a police siren that was coming from behind them. The regression equation that describes the relation between distance (feet) and age (year) was found to be: Distance = 500 – 3 Age a. Interpret the slope in terms of the problem. Be specific. b. Based on the equation, would the correlation be positive or negative? Explain. c. Should this equation be used to predict the distance that a 10 year old would first hear the police siren? Explain. 8. State whether the correlation in each of the following graphs is positive, negative, or equal to 0. 9. Suppose a modest relationship exists between two variables in a population. Would it be more likely to find a statistically significant relationship between a sample size of 40 or a sample size of 400? Explain. 10. Researchers at Penn State University found a positive correlation between weight loss (pounds) and typical distance walked (miles) by Penn State students on any given day. Explain why a conclusion that walking leads to weight reduction cannot be made from this study. 11. A regression equation that describes the relationship between the amount of the bill ($) at a restaurant and the tip ($) that was left is: Tip = 2.9 + 0.1 Bill a. For every increase in the bill by 1 dollar, how much additional tip should a server expect to receive? Does this suggest that customers, on the average are tipping at least 15%? Disregard the y-intercept in this analysis as it doesn’t have a logical interpretation (we would not have any data with amount of bill = $0) b. Use the regression plot found below (Figure A.8) to estimate (predict) the amount of tip that a server should expect when the restaurant bill is $60. Do not use the equation. c. The correlation between these two variables is .586 and has a p-value of .127. What conclusion can be made about the relationship between the amount of the bill and the tip that was left? Note that the x-axis (the horizontal axis) starts at $30 for Amount of Bill. Don’t be mislead by the plot. The y-intercept is indeed $2.90 and is obvious when you extend the x-axis to $0 Amount of Bill. This is why it is important to look at the starting values for the x and y axes before interpreting any regression plot.