Purdue University - Department of Statistics



STAT 113 Week 14 (Apr 8)Work Sheet 9: Chapter 14 & 15ScatterplotsThe gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon): Speed3040506070Mileage2024262420Make a scatterplot of mileage versus speed. The correlation between speed and mileage is r = 0. Explain why the correlation is 0 even though there is a strong relationship between speed and mileage. The relationship is nonlinear, correlation measures the strength of only straight-line association between two variables. Below is a scatterplot of grade on exam 2 versus time spent playing video games in hours for the Exam 2 week for 40 students. Describe the important features of the relationship between two variables:Form: linear or nonlinear?Linear Direction: positive or negative (or no association)? Negative Strength: strong, moderate, weak? Strong If we have an outlier like in the scatterplot below, will correlation increase, decrease or stay the same? correlation will decrease What should we do to see if the outlier is influential??Re-run the data without the outlier and see how much the slope and R^2 change.? If there are big changes, then the outlier is influential.Below is the Excel output for least-squares regression in Example 2: Regression StatisticsMultiple R0.900706456R Square0.81127212Adjusted R Square0.806305597Standard Error10.48251906Observations40ANOVA?dfSSMSFSignificance FRegression117949.2117949.21163.34812.47E-15Residual384175.562109.8832Total3922124.77????CoefficientsStandard Errort StatP-valueIntercept101.18374843.72817827.140271.75E-26Time-3.0110279470.23559-12.78082.47E-15What is the least squares regression line for this data? Be sure to identify your variables by name, not just x and y.y=101.18-3.01x, where y=Exam 2 grade and x=time spent playing video games in hours for the Exam 2 weekWhat does the intercept mean in terms of the story?The predicted value of Exam 2 grade for a student who does not play video games at all will be 101.18What does the slope mean in terms of the story?The predicted value of Exam 2 grade will decrease by 3.01 when the time spent playing video games increases by 1 hour. What is the predicted value of Exam 2 score for a student who plays 6 hours of video games during Exam 2 week? Is this a prediction or an extrapolation? Explain your answer.y=101.18-3.01*6=83.12This is a prediction because 6 is within the range of x-values in our dataWhat is the predicted value of Exam 2 score for a student who plays 33 hours of video games during Exam 2 week? Is this a prediction or an extrapolation? Explain your answer.y=101.18-3.01*33=1.85This is a extrapolation because 33 is outside of the range of x-values in our dataHow to interpret R-square in terms of the story? 81.13% of variation in the values of Exam 2 grade is explained by the least-squares regression What is the correlation between grade on exam 2 and time spent playing video games in hours for the Exam 2 week?-0.8113=-0.9007 or attach a negative sign to the “Multiple R” part of the output. In 1988, the Kalamazoo (Michigan) Symphony advertised a “Mozart for Minors” program with this statement: “Questions: Which students scored 51 points higher in verbal skills and 39 points higher in math? Answer: Students who had experience in music.” What do you think of the claim that “experience in music” causes higher test scores? Explain possible lurking variables that could be interfering.It is not appropriate to conclude that the relationship is due to cause and effect. Lurking variables might explain the relationship. Students with music experience might have other advantages (wealthier parents, better school systems…)This is best described as an example of: ConfoundingA valid conclusionCausationCommon responseDraw a circles-and-arrows diagram to demonstrate your answer.?x: experience in musicy: higher test scoresz: lurking variables (wealthier parents, better school systems…) Come up with a story not used in class or in the book that is an example of common response and another that is an example of confounding.?Draw a circles-and-arrows diagram to go with each story.?common response: during summer more people drink Coke (x) and also more people are drowned (y), it’s the warmer weather (z) that’s causing an increase in both. confounding : Joe got a good night's sleep(x) before his statistics exam, and he got an A on the exam (y). Sleep is important for mental focus, but so is studying, doing practice problems, etc (z). 2. ................
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