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Math Statistics An Introduction to Statistical Methods and Data Analysis

(a) To draw: The scatterplot of the given data. Given information: The data regarding dose level (independent variable) is shown below 2,2,2,4,4,8,8,16,16,16,32,32,64,64,64 For response (response variable) 5,7,3,10,14,15,17,20,21,19,23,29,28,31,30 Graph: The graph can be drawn using R Storing the above data in R dose.level<- c(2,2,2,4,4,8,8,16,16,16,32,32,64,64,64) response <- c(5,7,3,10,14,15,17,20,21,19,23,29,28,31,30) The code to draw the scatterplot is plot(x = dose.level, y = response) The plot obtained is attached below (b) To find: The regression line of the given set of data values. The required answer is y = 10.6188 + 0.3375 x Calculation: The regression model could easily be ibtained executing the below command in R. regression.model<- lm(response ~ dose.level) Obtained summary of the model summary(regression.model) From the above image, the intercept ( β 0 ) = 10.6188 and slope coefficient ( β 1 ) = 0.3375 . Using this, the regression model is y = β 0 + β 1 x y = 10.6188 + 0.3375 x (c) To draw: The residual plot of the above model. Graph: Extracting the residuals from the above model residuals <- regression.model$residuals Fitting a plot plot(fitted(regression.model), residuals) The plot is attached herewith. Interpretation: It can be seen that most of the residuals are on the left while only three are there on the right. The size is residuals is also large for three of them, two of them being below -5, and one of them being above 5. This shows that some adjustment needs to be done for a better fit.

(a) To draw: The scatterplot of the given data. Given information: The data regarding dose level (independent variable) is shown below 2,2,2,4,4,8,8,16,16,16,32,32,64,64,64 For response (response variable) 5,7,3,10,14,15,17,20,21,19,23,29,28,31,30 Graph: The graph can be drawn using R Storing the above data in R dose.level<- c(2,2,2,4,4,8,8,16,16,16,32,32,64,64,64) response <- c(5,7,3,10,14,15,17,20,21,19,23,29,28,31,30) The code to draw the scatterplot is plot(x = dose.level, y = response) The plot obtained is attached below (b) To find: The regression line of the given set of data values. The required answer is y = 10.6188 + 0.3375 x Calculation: The regression model could easily be ibtained executing the below command in R. regression.model<- lm(response ~ dose.level) Obtained summary of the model summary(regression.model) From the above image, the intercept ( β 0 ) = 10.6188 and slope coefficient ( β 1 ) = 0.3375 . Using this, the regression model is y = β 0 + β 1 x y = 10.6188 + 0.3375 x (c) To draw: The residual plot of the above model. Graph: Extracting the residuals from the above model residuals <- regression.model$residuals Fitting a plot plot(fitted(regression.model), residuals) The plot is attached herewith. Interpretation: It can be seen that most of the residuals are on the left while only three are there on the right. The size is residuals is also large for three of them, two of them being below -5, and one of them being above 5. This shows that some adjustment needs to be done for a better fit.

Solution Summary: The author explains how to draw the scatterplot of the given data using R.

An Introduction to Statistical Methods and Data Analysis

An Introduction to Statistical Methods and Data Analysis

7th Edition

ISBN: 9781305269477

Author: R. Lyman Ott, Micheal T. Longnecker

Publisher: Cengage Learning

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Chapter 11.9, Problem 39E

Chapter 11.9, Problem 41E

Chapter 11 Solutions

An Introduction to Statistical Methods and Data Analysis

Ch. 11.9 - Prob. 1E Ch. 11.9 - Refer to Exercise 11.1. Plot the equation in the...Ch. 11.9 - Use the data given here to answer the following...Ch. 11.9 - Prob. 4E Ch. 11.9 - Use the output from Minitab for these data to...Ch. 11.9 - A food processor was receiving complaints from its...Ch. 11.9 - An online retailer needs to manage the amount of...Ch. 11.9 - A manufacturer of cases for sound equipment...Ch. 11.9 - Refer to the data of Exercise 11.7. a. Calculate a...Ch. 11.9 - Refer to the data of Exercise 11.8. Calculate a...

Ch. 11.9 - Refer to the data of Exercise 11.8. Calculate a...Ch. 11.9 - Athletes are constantly seeking measures of the...Ch. 11.9 - A firm that prints automobile bumper stickers...Ch. 11.9 - A chemist is interested in determining the weight...Ch. 11.9 - Refer to Exercise 11.22 to complete the following....Ch. 11.9 - Prob. 40E Ch. 11.9 - A survey of MBA, graduates of a business school...Ch. 11.9 - Refer to the data in Exercise 11.44. Determine the...Ch. 11.9 - There has been an increasing emphasis in recent...Ch. 11.9 - An air conditioning company responds to calls...Ch. 11.9 - Refer to Exercise 11.61. a. Calculate the...Ch. 11.9 - Refer to Exercise 11.61. Test for lack of fit for...Ch. 11.9 - Refer to Exercise 11.61. Compute the standard...Ch. 11.9 - Prob. 93SE

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