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Name: _______________________________________________ Per: ____ Date: ______________Chapter 3 Problem Set A.P. StatisticsA student wonders if tall women tend to date taller men. She measures herself, her dormitoryroommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (heights in inches):Women666466657065Men726870687165Is there a clear explanatory variable and response variable in this setting? If so, tell which is which. If not, explain why not. Make a well-labeled scatterplot of these data.Based on the scatterplot, describe the pattern, if any, in the relationship between the heights of women and the heights of the men they date.Use your calculator to find the correlation r between the heights of the men and women. Do the data show any evidence that taller women tend to date taller men? Explain.How would r change if -all the men were 6 inches shorter than the heights given in the table? -heights were measured in centimeters rather than inches? (2.54 centimeters = 1inch.) f) Suppose another 70-inch-tall female who dated a 73-in-tall male were added to the data set. How would this influence r?Below is some data on the relationship between the price of a certain manufacturer’s flatpanel LCD televisions and the area of the screen. We would like to use these data to predict the price of televisions based on size.2266957937500 Screen Area (sq. inches)Price (dollars)154250207265289330437375584575683650a) Use your calculator to find the equation of the least-squares regression equation. Write the equation, defining any variables you use. b) Explain what is meant by “least squares” in the expression “least-squares regression line.” c) This manufacturer also produces a television with a screen size of 943 square inches. Would it be reasonable to use this equation to predict the price of that television? Explain. d) Calculate the residual for the television that has a screen area of 437 square inches. What does this number suggest about the cost of this television, relative to the others?Alana’s favorite exercise machine is a stair climber. On the “random” setting, it changes speeds at regular intervals, so the total number of simulated “floors” she climbs varies from session to session. She also exercises for different lengths of time each session. She decides to explore the relationship between the number of minutes she works out on the stair climber and the number of floors it tells her that she’s climbed. She records minutes of climbing time and number of floors climbed for six exercise sessions. Computer output and a residual plot from a linear regression analysis of the data are shown below.0000a) What is the equation of the least-squares line? Be sure to define any variables you use.b) Is a line an appropriate model for these data? Justify your answer.c) Interpret the value of s (S = 2.3472) in the context of this problem.0-190500Scientists studying outbreaks of locusts in Tanzania found a negative correlation between theamount of rainfall (in inches) in the wet season and the relative abundance of adult red locusts 18months later. (Relative abundance is measure on a 1 to 5 scale, where a “5” means five times asmany locusts as “1.”) The least-squares regression equation for this relationship is: Predicted relative abundance = 6.7 – 0.12(rainfall)Interpret the slope of this line in the context of the problem.The correlation between these two variables is –0.75. If the amount of rainfall were measured in centimeters rather than inches, how would the correlation change? Explain.Explain what “least-squares” means in term of the variables involved.Would it be appropriate for the scientists to conclude that changes in rainfall are responsible for variations in the relative abundance of red locusts in this region? Why or why not?Because elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height from height to the knee. Here are data (in centimeters) for five elderly men: Knee Height, cm. 57.7 47.4 43.5 44.8 55.2 Height, cm 192 153 146 163 169a) Which variable is explanatory and which is response in this situation?b) Construct a scatterplot on your calculator and draw a rough sketch of your calculator’s display. Describe the form, direction, and strength of the relationship that you see.c) Use your calculator to determine the least-squares regression line. Write the equation and define any variables you use.d) What are the slope of the LSRL and the value of r? Interpret both in context.e) Suppose a sixth elderly man with a knee height of 57 cm. and a height of 150 cm is added. What impact would this have on (a) the correlation and (b) the slope of the regression line?f) Should you use your regression line from (c) to predict the height of an elderly man whose knee height is 70 centimeters? If so, do it. If not, explain why not. ................
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