Unless otherwise specified, round all your answers to three decimal places. 1. Beer: In this example...

 

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Unless otherwise specified, round all your answers to three decimal places. 1. Beer: In this example we will use a dataset that has information on a random sample of 82 different beers. We have the Alcohol Content (units in %) and Calories (units in Cals). In this lab we will use JMP when necessary. As is often the case, the variables we are interested in working with do not always specifically lend themselves toward clear response variables or explanatory variables. In this case we will assume we are interested in answering the following question: Is it necessary to have beer with higher calories in order to get a higher alcohol content? This means we will classify the calories as the explanatory variable and the alcohol content will be the response variable. In this lab, you will use the utility in JMP, called Fit Model. Although you may answer several of the questions using Fit Y by X, it will be necessary to use Fit Model for a large portion of the lab. (a) Fit a simple linear regression model using Fit Model. Write down both the population model and the fitted simple linear regression model. Explain the symbols: y, ŷ, and x. Use the context of the example with your explanation. i. Population model: ii. Fitted model: iii. Explain the symbols: • fly ● ŷ ● X (b) Provide an interpretation of the R². (c) Check all four assumptions for this fitted model. Attach any appropriate graphs to your lab. Please label all of your graphs (example A, B, ...). For each assumption indicate which graph is used to check this assumption. Also indicate whether or not the assumption has been met. i. Independence: ii. Form of the Model (linear relationship): iii. Constant Variance Assumption: iv. Normality of the Errors: Unless otherwise specified, round all your answers to three decimal places. 1. Beer: In this example we will use a dataset that has information on a random sample of 82 different beers. We have the Alcohol Content (units in %) and Calories (units in Cals). In this lab we will use JMP when necessary. As is often the case, the variables we are interested in working with do not always specifically lend themselves toward clear response variables or explanatory variables. In this case we will assume we are interested in answering the following question: Is it necessary to have beer with higher calories in order to get a higher alcohol content? This means we will classify the calories as the explanatory variable and the alcohol content will be the response variable. In this lab, you will use the utility in JMP, called Fit Model. Although you may answer several of the questions using Fit Y by X, it will be necessary to use Fit Model for a large portion of the lab. (a) Fit a simple linear regression model using Fit Model. Write down both the population model and the fitted simple linear regression model. Explain the symbols: y, ŷ, and x. Use the context of the example with your explanation. i. Population model: ii. Fitted model: iii. Explain the symbols: • fly ● ŷ ● X (b) Provide an interpretation of the R². (c) Check all four assumptions for this fitted model. Attach any appropriate graphs to your lab. Please label all of your graphs (example A, B, ...). For each assumption indicate which graph is used to check this assumption. Also indicate whether or not the assumption has been met. i. Independence: ii. Form of the Model (linear relationship): iii. Constant Variance Assumption: iv. Normality of the Errors: