Simple Linear Regression problems: 1) ) When deciding to purchase a used car, a student looked at the number of years that the car has been on the road and the asking price. The following graph and data could be found. Complete all of the questions that follow the output. Scatterplot of price of car vs years driven 16000 14000 price of car 12000 10000 8000 6000 4000 2000 2 4 6 Predictor Constant years driven Coef 15481 -1139.1 S = 1545.03 R-Sq = (D)% 8 years driven SE Coef 1368 168.1 T 11.32 -6.78 10 12 P 0.000 0.000 R-Sq(adj) = 73.7% Analysis of Variance Source Regression Residual Error Total DF 1 15 16 SS 109601013 35806988 145408001 MS 109601013 2387133 F 45.91 P 0.000 a) What are the independent and dependent variables? b) Does the scatterplot indicate a relationship? If so, what kind? c) If you claim that there is a relationship, prove it using more than one technique. d) State the equation of the line and then define both the slope and the y-intercept. e) Find R-squared using the table. f) Find the MSE. g) Test to see if the there is evidence that the slope is significant. Set up the null and alternative and then test at =.05. h) If a car has been driven for 6 years, how much should it cost? Does this number seem reasonable? i)If a car is driven for 18 years, how much should is cost? Does this number seem reasonable? j) Is the point (3, $15500) an influential observation? Why or Why not? 1) A study was done on the age of babies (in months) and the amount of hours during the day (total) that they sleep in a 24 hour period. a) What are the independent and dependent variables? b) Does the scatterplot indicate a feasible relationship? Scatterplot of hours slept vs age (months) 15 hours slept 14 13 12 11 0 2 4 6 age (months) 8 10 12 c) Using the output, what is the equation of the line and define the slope and y intersept in terms of the problem. Predictor Constant age (months) S = 0.766528 Coef 15.0900 -0.25718 SE Coef 0.3874 0.05917 R-Sq = 49.9% T 38.95 -4.35 P 0.000 0.000 R-Sq(adj) = 47.2% Analysis of Variance Source Regression Residual Error Total DF 1 19 20 SS 11.099 11.164 22.263 MS 11.099 0.588 F 18.89 P 0.000 d) What percent of the variation in sleep can be explained by age? e) Test the slope. f) How long will a family with a 10 month old expect them to sleep