It is proposed that fuel efficiency (Y km/1) in motorway test conditions can be well modelled by a linear relationship with engine size (X litres). Eight cars drive a motorway test route and their engine size and fuel efficiency are recorded in the table below. The linear regression model can be written as Y = Bo + BIX +E X 1.10 1.10 1.20 1.20 1.40 1.40 1.60 1.60 Y 14.53 11.35 16.66 16.54 18.83 14.92 20.14 21.41 (a) Use the method of least squares to estimate the slope B1 and intercept Bo of the best fitting regression line to these data. (b) Calculate and interpret a 90% confidence interval for B1. (c) Calculate the coefficient of correlation for this model. Explain what the correlation coefficient measures. (d) Create sketches of scatter plots for the situations when: (a) The correlation coefficient is 0. (b) The correlation coefficient is -0.8. (e) Based on your answers to parts (a), (b) and (c), describe (in words) the relationship between fuel efficiency and engine size