Descriptive Statistics – Exercises 8 1. What do you mean by r=0 , r=1, r=-1 ? (2-5) (a) Draw a scatter diagram of the data (b) Compute the correlation coefficient (c) Determine whether there is a linear relation between x and y? 2. X y 3. 2 4 4 8 6 10 6 13 7 20 X y 4. 2 10 3 9 5 7 6 4 6 2 X y 5. 2 8 6 7 6 6 7 9 9 5 X Y 27 30 22 26 15 25 35 42 30 38 52 40 35 32 55 54 40 50 40 43 6. Does studying for an exam pay off? The number of hours studied x, is compared with the exam grade received y: X Y Find r. 2 80 Descriptive Statistics WS 2010/2011 5 80 1 70 4 90 2 60 1 7. A marketing firm wished to determine whether the no. of television commercials broadcast were linearly correlated with the sales of its product. The data, obtained from each of several cities, are shown in the following table: Commercials 12 x Sales, Units 7 y 6 9 15 11 15 8 16 12 6 5 10 14 12 9 6 11 11 8 Draw a scatter diagram and calculate r. 8. The national highway system is made up of interstate highways and non-interstate highways. Listed are 15 randomly selected US states and their corresponding no. of miles of interstate and noninterstate highway State AL VT NH RI AZ IA WI NY NE UT TX OK WV AK GA Descriptive Statistics WS 2010/2011 Interstate 905 320 235 71 1167 782 745 1674 482 940 3233 930 549 1082 1245 Non-interstate 2715 373 589 197 1565 2433 3404 3476 2496 1253 10157 2431 1195 1030 3384 2 a. Construct a scatter diagram using x= inter-state and y= non interstate miles. b. Describe the pattern displayed, including any unusual characteristics c. Calculate the correlation coefficient. d. Remove Texas from the data and repeat parts a through c. e. Compare the results. 9. An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various domestic cars and their gas mileages in the city for the 2008 model year. Car Weight Miles per Gallon 3765 19 3984 18 3530 21 3175 22 2580 27 3730 18 2605 26 3772 17 3310 20 2991 25 2752 26 a) Determine which variable is the likely explanatory variable and which is the likely response variable. b) Draw a scatter diagram of the data c) Compute r d) Does a linear relation exits between the weight of a car and its miles per gallon in the city? Descriptive Statistics WS 2010/2011 3 10. A doctor wanted to determine whether a relation exists between a male’s age and his HDL (so called good) cholesterol. He randomly selected 17 of his patients and determined their HDL cholesterol levels. He obtained the following data: Age HDL Cholesterol 38 57 42 54 46 34 32 56 55 35 52 40 61 42 61 38 26 47 38 44 66 62 30 53 51 36 27 45 52 38 49 55 39 28 a) Draw a scatter diagram of the data treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol? b) Compute the linear correlation coefficient between age and HDL cholesterol c) Does a linear relation exist between age and HDL cholesterol? Descriptive Statistics WS 2010/2011 4
