2   1. Kwame is investigating a possible relationship between average March temperature, t °C, and tea yield, y kg/hectare, for tea grown in a particular location. He uses 30 years of past data to produce the following summary statistics for a linear regression model, with tea yield as the dependent variable. Residual Sum of Squares (RSS) = 1 666 567        Stt = 52.0        Syy = 1 774 155 least squares regression line:        gradient = 45.5        y-intercept = 2080 (a) Use the regression model to predict the tea yield for an average March temperature of 20 °C (1) He also produces the following residual plot for the data. 23 22 21 20 19 18 17 Temperature (t °C) 800 600 400 200 0 –200 –400 –600 Residual (b) Explain what you understand by the term residual. (1) (c) Calculate the product moment correlation coefficient between t and y (2) (d) Explain why the linear model may not be a good fit for the data (i) with reference to your answer to part (c) (ii) with reference to the residual plot. (2) Question 1 continues on page 4 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 3   Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________