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1. Researchers found that the speed of a prey (twips/s) and the length of prey (twips x 100) are good predictors of the time (s) required to catch a prey. (A twip is a measure of distance used by programmers). Data were collected in an experiment in which subjects were asked to "catch" an animal prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which prey moved across the screen. {r} prey <- read.csv("https://www.siue.edu/-jpailde/prey.csv") prey i) Fit a multiple regression model for predicting catch time using prey length and speed as predictors. ii) Construct 95\% confidence interval for the regression slopes of each predictor. Interpret your result. Will the interpretation change if you change the confidence level to 90\% and 99\%? iii) Predict the catch time for two animals whose lengths are 4 and 6; and whose speeds are 30 and 60, respectively. State your result in paragraph form including the associated prediction intervals. iv) Is the multiple regression model useful for predicting catch time? Use `R2`, `adj-R2`, and test the relevant hypothesis using alpha = 0.05. State your conclusion. v) The primary researchers suggest that a simple regression model with the single predictor length/speed might be a better model for predicting catch time. Calculate and add the `x values to the data using the function `mutate` in the package `dplyr`. Fit a simple linear regression model using the new variable/column `x`. vi) Which of the two models considered (the multiple regression model in part (i) or the simple regression model in part (v)) would you recommend for predicting catch time? Justify your choice.

1. Researchers found that the speed of a prey (twips/s) and the length of prey (twips x 100) are good predictors of the time (s) required to catch a prey. (A twip is a measure of distance used by programmers). Data were collected in an experiment in which subjects were asked to "catch" an animal prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which prey moved across the screen. {r} prey <- read.csv("https://www.siue.edu/-jpailde/prey.csv") prey i) Fit a multiple regression model for predicting catch time using prey length and speed as predictors. ii) Construct 95\% confidence interval for the regression slopes of each predictor. Interpret your result. Will the interpretation change if you change the confidence level to 90\% and 99\%? iii) Predict the catch time for two animals whose lengths are 4 and 6; and whose speeds are 30 and 60, respectively. State your result in paragraph form including the associated prediction intervals. iv) Is the multiple regression model useful for predicting catch time? Use `R2`, `adj-R2`, and test the relevant hypothesis using alpha = 0.05. State your conclusion. v) The primary researchers suggest that a simple regression model with the single predictor length/speed might be a better model for predicting catch time. Calculate and add the `x values to the data using the function `mutate` in the package `dplyr`. Fit a simple linear regression model using the new variable/column `x`. vi) Which of the two models considered (the multiple regression model in part (i) or the simple regression model in part (v)) would you recommend for predicting catch time? Justify your choice.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Researchers found that the speed of a prey (twips/s) and the length of prey (twips x 100) are good predictors of the time (s) required to catch a prey. (A twip is a measure of distance used by programmers). Data were collected in an experiment in which subjects were asked to "catch" an animal prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which prey moved across the screen. {r} prey <- read.csv("https://www.siue.edu/-jpailde/prey.csv") prey i) Fit a multiple regression model for predicting catch time using prey length and speed as predictors. ii) Construct 95\% confidence interval for the regression slopes of each predictor. Interpret your result. Will the interpretation change if you change the confidence level to 90\% and 99\%? iii) Predict the catch time for two animals whose lengths are 4 and 6; and whose speeds are 30 and 60, respectively. State your result in paragraph form including the associated prediction intervals. iv) Is the multiple regression model useful for predicting catch time? Use `R2`, `adj-R2`, and test the relevant hypothesis using alpha = 0.05. State your conclusion. v) The primary researchers suggest that a simple regression model with the single predictor length/speed might be a better model for predicting catch time. Calculate and add the `x values to the data using the function `mutate` in the package `dplyr`. Fit a simple linear regression model using the new variable/column `x`. vi) Which of the two models considered (the multiple regression model in part (i) or the simple regression model in part (v)) would you recommend for predicting catch time? Justify your choice.
Transcribed Image Text:1. Researchers found that the speed of a prey (twips/s) and the length of prey (twips x 100) are good predictors of the time (s) required to catch a prey. (A twip is a measure of distance used by programmers). Data were collected in an experiment in which subjects were asked to "catch" an animal prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which prey moved across the screen. {r} prey <- read.csv("https://www.siue.edu/-jpailde/prey.csv") prey i) Fit a multiple regression model for predicting catch time using prey length and speed as predictors. ii) Construct 95\% confidence interval for the regression slopes of each predictor. Interpret your result. Will the interpretation change if you change the confidence level to 90\% and 99\%? iii) Predict the catch time for two animals whose lengths are 4 and 6; and whose speeds are 30 and 60, respectively. State your result in paragraph form including the associated prediction intervals. iv) Is the multiple regression model useful for predicting catch time? Use `R2`, `adj-R2`, and test the relevant hypothesis using alpha = 0.05. State your conclusion. v) The primary researchers suggest that a simple regression model with the single predictor length/speed might be a better model for predicting catch time. Calculate and add the `x values to the data using the function `mutate` in the package `dplyr`. Fit a simple linear regression model using the new variable/column `x`. vi) Which of the two models considered (the multiple regression model in part (i) or the simple regression model in part (v)) would you recommend for predicting catch time? Justify your choice.
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