SECTION B: CORRELATION AND REGRESSION Question B1 [2 marks] For each of the datasets displayed in the scattergraphs below (questions B1 parts 1) and 2)), choose the number from the following list which is the mostly likely value of the product moment correlation coefficient, r. List: -3 -1 -0.85 -0.5 0 0.5 0.85 1 3 1) 90 80 ROROSO 200 70 60 50 40 30 r = Choose the most appropriate value from the list above/nQuestion B2 [3 marks] You are investigating the effect of advertising on the sales of a product. You draw a scatter plot and obtain the regression line y = 3.7 +1.5x where x is the amount spent on advertising and y is the value of sales. 1) State the the y-intercept of this regression line. 2) For each of the two following statements decide if you think the statement is TRUE or FALSE "The y-intercept is the value of sales when no money is spent on advertising." "The gradient is the increase in the value of sales when one more unit is spent on advertising." First Second If you think: First Second then Enter TRUE TRUE 1 TRUE FALSE 2 FALSE TRUE 3 FALSE FALSE 4 (1, 2, 3 or 4)/nQuestion B3 [4 marks] The following data was collected about second-hand cars giving the mileage ('000s) denoted by x and the price (in £000s) denoted by y. (There are 8 data pairs so n = 8.) [Use x= 21 etc and y= 6.5 etc throughout. You do not need x= 21000 etc, y= 6500 etc] Car A B с D E F G H X 21 74 96 44 55 12 74 36 y 6.5 3.9 1.1 4.2 3.8 7.5 2.8 5.4 Calculate: 1) the correlation coefficient, r (to 3 dp) to 3 dp 2) the coefficient of determination, R², giving your answer as a percentage (eg 98.6%). to 1 dp. The equation of the regression line is y = A + Bx, calculate (to 4dp) the values of: 3) B to 4 dp 4) A to 4 dp/nQuestion B4 [2 marks] 200 workers aged between 20 and 55 years were interviewed in a survey investigating the possible relationship between age and salary. The correlation coefficient was 0.872 and the regression line was: Salary = 12100 + 440 × (Age in years). 1) Use the regression line to predict the salary of a 30 year old. 2) Decide whether the following statements are TRUE or FALSE. First: The intercept is meaningful for this regression line. Second: Using the regression line to predict the salary of a 47 year old is fairly reliable. If you think: First Second then Enter TRUE TRUE 1 TRUE FALSE 2 FALSE TRUE 3 FALSE FALSE 4 (1, 2, 3 or 4)

Fig: 1

Fig: 2

Fig: 3

Fig: 4