3. Sporty cars are designed to provide better handling, acceleration, and a more responsive driving experience than a typical sedan. But, even within this select group of cars, performance as well as price can vary. Consumer Reports provided road- test scores and prices for the following 10 sporty cars. Prices are in thousands of dollars and road- test scores are based on a 0- 100 rating scale, with higher values indicating better performance. Car Price ($1000s) Road-Test Score Chevrolet Cobalt SS 24.5 78 Dodge Caliber SRT4 24.9 56 Ford Mustang GT (V8) 29.0 73 Honda Civic Si 21.7 78 Mazda RX-8 31.3 86 Mini Cooper S 26.4 74 Mitsubishi Lancer Evolution GSR 38.1 83 Nissan Sentra SE-R Spec V 23.3 66 Suburu Impreza WRX 25.2 81 Suburu Impreza WRX Sti 37.6 89 a) Develop a scatter diagram with price as the independent variable. b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c) Develop the estimated regression equation. Write down the estimated regression equation for this problem Provide an interpretation for the slope of the estimated regression equation. (Pay attention to Units while answering the question). e) Another sporty car that Consumer Reports tested is the BMW 135i; the price for this car was $ 36,700. Predict the road- test score for the BMW 135i using the estimated regression equation developed (Pay attention to Units while answering the question). f) Find the 98% Confidence and Prediction Intervals for the BMW 135i in part (e). Conduct p-Value as well as Critical-Value based Hypothesis Tests to determine the significance of regression. Use o = 0.01. Is the regression statistically significant