3. Setup: The data set "Healthy Breakfast" contains, among other variables, the Consumer Reports ratings of 77 cereals and the number of grams of sugar contained in each serving. (Data source: Free publication available in many grocery stores. Data set available through the Statlib Data and Story.) Considering "Sugars" as the explanatory variable and "Rating" as the response variable generated the following regression line: Rating = 59.3-2.40 - Sugars. and the ANOVA table Source Regression Error Total SS df MS 8654.7 1 8654.7 102.35 6342.1 75 84.6 14996.8 76 F Questions: (a) Write down the simple linear regression model and its model assumption. (b) State the null and alternative hypotheses for the model. Based on the ANOVA table, draw conclusion based on the p-value for the test. (c) Obtain szz and the standard error se (3₁) to construct the 95% confidence interval for $₁.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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3. Setup:
The data set "Healthy Breakfast" contains, among other variables, the Consumer Reports
ratings of 77 cereals and the number of grams of sugar contained in each serving. (Data
source: Free publication available in many grocery stores. Data set available through the
Statlib Data and Story.) Considering "Sugars" as the explanatory variable and "Rating"
as the response variable generated the following regression line:
Rating = 59.3-2.40 - Sugars.
and the ANOVA table
Source
Regression
Error
Total
SS df
MS
8654.7 1 8654.7 102.35
6342.1 75 84.6
14996.8 76
F
Questions:
(a) Write down the simple linear regression model and its model assumption.
(b) State the null and alternative hypotheses for the model. Based on the ANOVA table,
draw conclusion based on the p-value for the test.
(c) Obtain Srz and the standard error se (3₁) to construct the 95% confidence interval
for $₁.
Transcribed Image Text:3. Setup: The data set "Healthy Breakfast" contains, among other variables, the Consumer Reports ratings of 77 cereals and the number of grams of sugar contained in each serving. (Data source: Free publication available in many grocery stores. Data set available through the Statlib Data and Story.) Considering "Sugars" as the explanatory variable and "Rating" as the response variable generated the following regression line: Rating = 59.3-2.40 - Sugars. and the ANOVA table Source Regression Error Total SS df MS 8654.7 1 8654.7 102.35 6342.1 75 84.6 14996.8 76 F Questions: (a) Write down the simple linear regression model and its model assumption. (b) State the null and alternative hypotheses for the model. Based on the ANOVA table, draw conclusion based on the p-value for the test. (c) Obtain Srz and the standard error se (3₁) to construct the 95% confidence interval for $₁.
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