Breakfast cereals again We saw in Chapter 7 that thecalorie count of a breakfast cereal is linearly associatedwith its sugar content. Can we predict the calories of aserving from its vitamin and mineral content? Here’s amultiple regression model of Calories per serving on itsSodium (mg), Potassium (mg), and Sugars (g):Dependent variable is CaloriesR-squared = 38.4, R-squared (adjusted) = 35.9,s = 15.60 with 77 - 4 = 73 degrees of freedomSource Sum ofSquares dfMeanSquare F-Ratio P-ValueRegression 11091.8 3 3697.28 15.2 60.0001Residual 17760.1 73 243.289Variable Coefficient SE(Coeff) t-Ratio P-ValueIntercept 83.0469 5.198 16.0 60.0001Sodium 0.05721 0.0215 2.67 0.0094Potass -0.01933 0.0251 -0.769 0.4441Sugars 2.38757 0.4066 5.87 60.0001Assuming that the conditions for multiple regressionare met,a) What is the regression equation?b) Do you think this model would do a reasonably goodjob at predicting calories? Explain.c) Would you consider removing any of these predictorvariables from the model? Why or why not?d) To check the conditions, what plots of the data mightyou want to examine?

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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.