Post at least one statement about two numerical variables that you believe to have a relationship between them. Explain how you would assess the strength and direction of the relationship. How could...

Homework math


Post at least one statement about two numerical variables that you believe to have a relationship between them.  Explain how you would assess the strength  and direction of the relationship.  How could you make predictions about this relationship? 1) A college statistics instructor wanted to investigate the relationship between age (in years) and a measure of flexibility. Flexibility was measured by asking a person to bend at the waist as far as possible, extending his or her arms toward the floor. Using a yardstick, the distance from the floor to the fingertip closest to the floor was measured (in inches). Negative measurements indicate going beyond just touching the floor. Age and the measure of flexibility just described was measured for a group of 28 students in the instructor’s class. The goal was to determine if there is a relationship between age and this measure of flexibility. What are two reasons why it would not be a good idea to use just the students in your class as the subjects for your study? 2) The table below shows the data collected. Use it to construct a scatter plot, either manually, or by pasting a screenshot from a graphing tool such as Statext, Desmos, Google sheets, a graphing calculator, etc. Comment on any interesting features of the plot. Does it look like there is a relationship between age and flexibility? If so, what kind? If not, why not? 3) Find the correlation coefficient and the Least Squares Regression Line for the data from the table. Comment on the strength and direction of the relationship. What would be your prediction for the measure of flexibility of a student who is 35 years old? 4. (50 points) Baseball teams win and lose games. Many fans believe that a team’s earned run average (ERA) has a major effect on that team’s winning. During the 2008 season, the 30 Major League Baseball teams recorded the numbers of wins along with the corresponding earned run averages. The data are in the table below, along with a scatterplot and a Minitab readout. Predictor Coef SE Coef T P Constant 152.6116 14.9628 10.1994 0.0000 ERA -16.6050 3.4483 -4.8155 0.0000 S = 8.3440 R-sq = 45.3% R-sq(adj) = 43.3% (a) Does the scatterplot suggest that teams tend to win more games when their team ERA is lower? Explain why or why not. What numerical measure could you use to reinforce your argument? Page 1 of 4 (b) What is the equation of the least squares line describing the relationship between ? = ERA and ? = Wins? What number of wins would you predict for a team with an ERA of 3.75? (c) On the average, how is the number of wins affected by an increase of 1 in the ERA? Explain how you determined this number. (d) What proportion of the variation in the number of wins is explained by the ERA? Page 2 of 4 5. (50 points) As early as 3 years of age, children begin to show preferences for playing with members of their own sex, and report having more same-sex than opposite-sex friends. In a study of 3rd and 4th graders' views on 48 personality traits, children were asked to rate on a "5-point" scale: -2 = "someone possessing that trait is probably a boy" -1 = "someone possessing that trait might be a boy" 0 = "can't tell" 1 = "someone possessing that trait might be a girl" 2 = "someone possessing that trait is probably a girl" A plot of the data is presented below. A single point represents the (average girls' rating, average boys' rating) for a given trait. What proportion of the variability in a male’s rating is explained by a female’s rating? Page 2 of 4