SAJC Check your Understanding for Linear Regression_Teachers

Check your Understanding (Correlation and Linear Regression) MUTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1. In regression analysis, the variable that is being predicted is A the independent variable B the dependent variable C usually denoted by x D none of the above (B) 2. In the regression equation y = bo + b1x, bois the A slope of the line B independent variable C y intercept D none of the above (C) 3. In the regression equation y = bo + b1x, b1 is A the slope of the line B an independent variable C the y intercept D none of the above (A) 4. In regression analysis, the variable that is doing the predicting or explaining is A the independent variable B usually denoted by y C the dependent variable D none of the above (A)

5. The range of the correlation coefficient is A 0 to +1 B -1 to 0 C -1 to 0 D -1 to +1 (D) 6. If the slope of the regression equation y = bo + b1xis positive, then A as x increases y decreases B as x increases so does y C Either a or b is correct D none of the above (B) Scatter Diagram and Product Moment Correlation Coefficient 1. MI H1 Prelim 2017/Q11 An electric heater was switched on in a cold room and the temperature of the room was noted at five-minute intervals. Time from switching on electric heater, x (min) 0 5 10 15 20 25 30 35 40 Temperature of room, y (oC) 0.4 1.5 3.4 5.5 7.7 9.7 11. 7 13. 5 15. 4 (i) Draw a sketch of the scatter diagram for the data, as shown on your calculator. [2] (ii) Find the product moment correlation coefficient and comment on its value in the context of the data. [2] Answers (ii) 0.999 Solution:

1 (i) (ii) From graphing calculator, required coefficient, r ≈ 0.99870 = 0.999. (3 s.f) Since r > 0 and |r| = 0.999 is very close to 1, the value of r suggests that there is a strong positive linear correlation between the temperature of the room and the time from switching on the electric heater. 2. SAJC H1 Prelim 2017/Q7 (a) Eight pairs of values of variables x and y are measured. Draw a sketch of a possible scatter diagram of the data for each of the following cases: (i) the product moment correlation coefficient is approximately − 0.9, [1] (ii) the product moment correlation coefficient is approximately zero. [1] (b) A researcher recorded the water temperature T, in oC, and the depth D, in metres, at noon on a certain day at each of the eight locations in a lake. The results are summarized in the table below. D (m) 10 50 80 120 200 250 340 400