MATH 221 Week 7 Homework; Statistics for Decision-Making

1. Question: Two variables have a negative linear correlation. Does the dependent variable increase or decrease as the independent variable increases? 2. Question: What does the variable µ represent? 3. Question: A golfer wants to determine if the type of driver she uses each year can be used to predict the amount of improvement in her game. Which variable would be the response variable? 4. Question: Two variables have a positive linear correlation. Is the slope of the regression line between these two variables positive or negative? 5. Question: A value of the slope of the regression line would be given the notation of: 6. Question: If there is a ˆ, or hat, above a variable, what does that mean? 7. Question: Which of the following graphs displays the regression line of ŷ=0.75x + 3.34? 8. Question: Find the regression equation for the following data set 9. Question: A data set whose original x values ranged from 41 through 78 was used to generate a regression equation of ŷ=5.3x – 21.9. Use the regression equation to predict the value of y when x=45. 10. Question: A data set whose original x values ranged from 120 through 351 was used to generate a regression equation of ŷ=0.06x + 14.2. Use the regression equation to predict the value of y when x=115. 11. Question: Find the regression equation for the following data set 12. Question: A data set whose original x values ranged from 137 through 150 was used to generate a regression equation of ŷ=-4.5x + 51. Use the regression equation to predict the value of y when x=145. 13. Question: If the linear correlation coefficient is 0.681, what is the value of the coefficient of determination? 14. Question: If the linear correlation coefficient is -0.654, what is the value of the coefficient of determination? 15. Question: If the coefficient of determination is 0.184, what percentage of the data about the regression line is explained? 16. Question: If the coefficient of determination is 0.298, what percentage of the data about the regression line is unexplained? 17. Question: If the independent variables explained less than 50% of the variation in the dependent variables, which of the following would be true? 18. Question: The equation used to predict how tall a dog will be as an adult is ŷ=4.5 + 0.7x + 0.55x, where x is the height of the mother and x is the height of the father. Use this equation to predict the height of a puppy whose mother is 41.3 inches tall and whose father is 44.9 inches tall. 19. Question: The equation used to predict how long it will take to receive a package through the mail is ŷ=0.5 + 0.02x1 + 0.85x2 days, where x1 is the distance to travel and x2 is the weight of the package. Use this equation to predict the how long it will take to receive a package that is 249 miles away and weighs 2.1 pounds. 20. Question: The equation used to predict how long a cold will last is ŷ=-1.8 + 0.09x1 + 3.2x2 – 1.9x3, wherex1is person’s temperature on the first day, x2is number of people seen each day, andx3is the amount of sleep the person gets. Use this equation to predict how long a cold will last with a temperature of 100.8 degrees, an average of 3 people seen each day, and 6 hours of sleep.