Linear Models - Overview and Key Concepts

Linear model commonly known as predictive analysis is used to determine the outcome variable using the predictor variable ( Fox, 2015) . The model with the help of the independent variable accounts for the variability in the changes in the response variable ( Fox, 2015) . This model explains the relationship between the and independent variable and response variable. The model (in form of an equation) can be used to predict the other outcome when given different values of independent variables ( Fox, 2015) . In this study, we will focus on calories and fat content of eight different breakfast cereal. In this case, the calories are our dependent variable while the fat content is the dependent variable ( Fox, 2015) . The regression equation will show how the calories and the fat content are related, how the fat content can be used to predict calories in the eight brands in breakfast calories ( Fox, 2015) . To have different values of fat content, we will use different values of grams of breakfast cereals per serving. 

The most straightforward equation model that will be used will contain the independent variable, coefficients, and the dependent variables. Therefore, the equation will be of the form 

Y is the calories which is the estimated dependent score while beta zero and one are the constants, also known as the regression coefficients, and x is the fat content which the independent variable. 

Three main uses of the above regression model will help us to determine the regression analysis such as trend forecasting, forecasting an effect, and for causal analysis. 

One of the assumption made in this linear model is there need to a correlation between the variables. The relationship focuses on the strength of correlation between the one dependent variable and one or more independent variable(s). If the correlation between fat content and the calories to the eight brands is nearing one, then the line of the best fit will be diagonally straight starting from the origin ( Fox, 2015) . 

Using the line of the best fit, other measurement calories can be determined when the line is extrapolated. 

For this analysis, we will focus on Weetabix from 8 different companies baring different brand names. For different servings are used to determine four different fat contents. One serving is equivalent to 2 biscuits per 37.5 grams. The fat content is 0.8 and calories is 134.3. For 100grams of Weetabix, fat content is 2 and calories is 358. Two-third of the serving is equivalent to 25 grams with 0.53 fat content and 89.53 calories. Two serving has 75 grams with 1.6 fat content and 268.6 calories. Calorie is a standard measure used in measuring energy. The other brands used for comparison include Alpen Brars, Ready Brek, Weetos, Crunchy Bran, Oaty Bars, Weeaflakes, Alpen Weetabix On The Go, and Oatibix. The other nutrition per serving include carbohydrate, fiber, protein, and alcohol. Since all brands listed above have the almost the same calories and fat content per serving, we will use Weetabix to determine the linear model that will be used to determining the calories that is not occurring in our dataset. 

The linear model equation is 

The correlation of the two variables is nearing one. Therefore, there is a strong positive correlation between the two variables ( Fox, 2015) . Increase in fat content results to increase in calories. The coefficients are -8.9393 and 179.75 for beta zero and one respectively. 

From the model , we can estimate or predict other values of calories that have not been involved in the construction of the linear regression model. For instance, if we want to estimate the calories whose fat content is 3, we simply insert 3 in the equation to have 

The value obtained is realistic since we expected the value of calories to be greater than the one provided in the table above for the value of fat content (3) is also greater than the values provided in the table. Increase in fat content results to increase in calories ( Westman, 2010) . From the graph not all the points lie in the line of best fit, therefore, some of the brands have slightly different "filler" than others. 

We can, therefore, conclude that the linear model is helpful in predicting other values that are not in the table. The values can be obtained in the above graph when extrapolated or interpolated. Interpolation is for the values within the interval while extrapolation is for the values outside the interval ( Kutner, Nachtsheim, & Neter, 2004) . 

Works Cited 

Fox, J. (2015).  Applied regression analysis and generalized linear models . Sage Publications. 

Kutner, M. H., Nachtsheim, C., & Neter, J. (2004).  Applied linear regression models . McGraw-Hill/Irwin. 

WESTMAN, K. Calories Protein Fat.