\fDATAfile: Coasters A statistical program is recommended. You may need to use the appropriate technology to answer this question. The included data file contains characteristics of 61 coasters across the US and the rest of the world. You have been asked to create a model that predicts the duration of a ride (seconds) given its length (ft), top speed (mph), height (ft), drop (ft), and whether the ride includes an inversion. Note: an inversion is a roller coaster element in which the track turns riders upside-down and then returns them to an upright position. Use multiple regression to answer the following questions (=) Develop an estimated regression equation that can be used to predict the duration of a ride given the entire set of independent variables. Use x, for length, x, for top speed, x, for height, x, for drop, and x, to account for the presence of an inversion. (Round your numerical values to three decimal places.) y = Enter the following regression statistics. (Enter both coefficients of determination as percentages and round all your answers to one decimal place) R Square: Adjusted R Square: Standard Error: seconds (b) Use the estimated regression equation to predict the duration of a 6,000 ft ride that has an inversion, reaches a top speed of 90 mph, a height of 300 ft, and drops 250 ft. (Round your answer to one decimal place.) seconds (c) Use the Excel Data Analysis Correlation tool to develop a correlation table for the variables Top Speed (x, ), Height (x,), and Drop (x,) only. Enter the correlation coefficients in the following table. (Round your ar swers to three decimal places. Top Speed Height Height Drop Do the correlation coefficients provide evidence of multicollinearity among the variables top speed, height, and drop? Explain your reasoning. --.Select- out of three correlation coefficients are larger than 0.9, indicating the presence of multicollinearity between the following pairs of variables: Height vs. Top Speed Drop vs. Top Speed Drop vs. Height A ride -Select- v to climb higher to create a [-Select--. drop, and a ride [-Select-. a larger drop to reach a [--Select- v ] top speed. (d) Backward elimination is a variable selection technique used in multiple regression analysis that removes one variable at a time, starting with the coefficient with the largest p-value that is greater than a given threshold value, and continuing until either the model's adjusted coefficient of determination is maximized or all coefficient p-values are less than the threshold value. Consider the model you developed in part (a), and use backward elimination with a p-value threshold of 0.2 to develop an improved estimated regression equation that can be used to predict the duration of a ride. Keep the same variable names used in part (a). (Round your numerical values to three decimal places.) y = Enter the following regression statistics. (Enter both coefficients of determination as percentages and round all your answers to one decimal place.) R Square: Adjusted R Square: Standard Error: seconds Compare the regression statistics for the improved regression model vs. the original ones you entered in part (2). How have they changed? R Square: -Select-- v Adjusted R Square: -.Select Standard Error (e) Use the improved estimated regression equation you developed in part (d) to predict the duration of a ride having the same variable values you entered in part (b). Ignore any variable value that is no longer present in the improved estimated regression equation. (Round your answer to one decimal place.) seconds