A study was done to determine the relationship between the alcohol content of beer, and the amount of calories in a 12 oz serving size. The sample data is provided in the data below. a) From this sample data, can you conclude (at the alpha=0.05 level) that there is in fact a linear correlation between the two variables? Use the statistics (correlation coefficient, value) to describe the correlation (if any). B) Using the sample data, find a regression equation to estimate the number of calories in a beer. C) Dogfish Head Brewery in Milton, Delaware has an I.P.A. beer called "120 minute IPA" which has an alcohol content of 18%. Using your regression equation, estimate the number of calories in a 12 oz serving of 120 Minute. Brand/Beer Alcohol Content (%) Calories (per 12 oz) Big Sky Scape Goat Pale Ale 4.70 163 Sierra Nevada Harvest Ale 6.70 215 Steel Reserve 8.10 222 Coors Light 4.15 104 Genesee Cream Ale 5.10 162 Sierra Nevada Summeefest Beer 5.00 158 Michelob Beer 5.00 155 Flying Dog 4.70 158 Big Sky I.P.A. 6.20 195
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A study was done to determine the relationship between the alcohol content of beer, and the amount of calories in a 12 oz serving size. The sample data is provided in the data below.
a) From this sample data, can you conclude (at the alpha=0.05 level) that there is in fact a
B) Using the sample data, find a regression equation to estimate the number of calories in a beer.
C) Dogfish Head Brewery in Milton, Delaware has an I.P.A. beer called "120 minute IPA" which has an alcohol content of 18%. Using your regression equation, estimate the number of calories in a 12 oz serving of 120 Minute.
| Brand/Beer | Alcohol Content (%) | Calories (per 12 oz) |
| Big Sky Scape Goat Pale Ale | 4.70 | 163 |
| Sierra Nevada Harvest Ale | 6.70 | 215 |
| Steel Reserve | 8.10 | 222 |
| Coors Light | 4.15 | 104 |
| Genesee Cream Ale | 5.10 | 162 |
| Sierra Nevada Summeefest Beer | 5.00 | 158 |
| Michelob Beer | 5.00 | 155 |
|
Flying Dog |
4.70 | 158 |
| Big Sky I.P.A. | 6.20 | 195 |
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