Explanation Given info: The data related to the number of minutes the kids stayed at the table and the number of calories kids consumed. Calculation: Assumption for regression inferences: Population regression plane: There exists constants β 0 , β 1 , ... , β k and the predictor variables are x 1 , x 2 , ... , x k such that the conditional mean of the response variable ( y ) is β 0 + β 1 x 1 + ... + β k x k , the population regression equation y = β 0 + β 1 x 1 + ... + β k x k , the graph of which is known as a population regression plane. Equal standard deviations: For all of the predictor variables x 1 , x 2 , ... , x k response variable ( y ) has same conditional standard deviation ( σ ). Normal populations: The conditional distribution of the response variable ( y ) is normal distribution for each of the predictor variables x 1 , x 2 , ... , x k . Independent observations: The response variable takes values that are independent on each other. The conditions for a scatterplot that is well fitted for the data are, Straight Enough Condition: The relationship between y and x straight enough to proceed with a linear regression model. Outlier Condition: No outlier must be there which influences the fit of the least square line. Thickness Condition: The spread of the data around the generally straight relationship seem to be consistent for all values of x . From the given scatterplot, it can be said that the relation between consumed calories and time is negative and moderately linear. It can be concluded that, if a kid spent longer time at the table, consumed fewer calories than who left the table quickly. The relationship between calories and time is straight enough to precede a linear regression equation. Linear regression model: A linear regression model is given as y ^ = b 0 + b 1 x where be the predicted values of response variable and x be the predictor variable

Intro Stats, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780134210285

Author: Richard D. De Veaux, Paul Velleman, David E. Bock

Publisher: PEARSON

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Chapter R, Problem 2.37RE

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Chapter R, Problem 2.36RE

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Chapter R Solutions

Intro Stats, Books a la Carte Edition (5th Edition)

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Solution Summary: The author creates a regression equation model and interprets the data. The conditional distribution of the response variable (y) is normal distribution.

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