\fA statistical program is recommended. You may need to use the appropriate technologvto answerthis question. The included data le contains characteristics of 61 masters across the US and the rest of the world. You have been asked to create a rnodel that predicts the duration of a ride (seconds) given its length (it), top Speed [mph]. height (H), drop (). and whether the ride includes an inversion. Note: an Inversion is a roller coaster eiernent in which the track turns riders upsidesdown and then returns them to an upright position. Lise multiple regression to answer the following questions. to) Develop an estimated regression equation that can be used to predict the duration or a ride given the entire set of independent variables. Use x, ror ieneth, x2 for top speed, x3 rer height, x4 ror drop. and x5 to account for the presence of an inversion. (Round vour numerical values to three decimal places.) p: Enter the following regression statistics. [Enter both coekienls of determination as percentages and round all your answers to one decimal place) R Square: D/o Adjusted it Square: % Standard Error. seconds (ll) Use the estimated regression equation to preditt the duration of a 6,000 it ride that has an inversion, reaches a top speed of 90 mph, 3 height of 300 ft, and drops 250\" [Round your answer to one dedrnal place.) seconds (0 Use the Excel Data Analysis Correlation tool to develop a correlation table torthe variables Top Speed (x2), Height (x3), and Drop (x4) only Enter the correlation coefcients in the following table. [Round Your answers to three decimal places.) ran Speed Height Height 1 Drop Do the correlation coefficients provide evidence or multitollinearitv among the variables top speed, height. and drop? Explain vodr reasoning. Trliee v V, out of three correlation (oefcients are larger than 0.9, indicating the presence of multicoiiinean'ty petween the following pairs orvarisuies: i I Height v5. Top Speed i I Drop vs. Top Speed l | Drop us. Height Aride needs v o to ciirnp hidherto createa larger v J dreo,andande needs v ./ alarqererDlpreacha higher ~ 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 (a). How have they changed? R Square: decreased v Adjusted R Square: increased v Standard Error: decreased v 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