Breakfast cereals We saw in Chapter 7 that the calorie con-tent of a breakfast cereal is linearly associated with its sugar content. Is that the whole story? Here’s the output of aregression model that regresses Calories for each serving onits Protein(g), Fat(g), Fiber(g), Carbohydrate(g), andSugars(g) content.Dependent variable is CaloriesR-squared = 84.5, R-squared (adjusted) = 83.4,s = 7.947 with 77 - 6 = 71 degrees of freedomSource Sum ofSquares dfMeanSquare F-RatioRegression 24367.5 5 4873.50 77.2Residual 4484.45 71 63.1613Variable Coefficient SE(Coeff) t-Ratio P-ValueIntercept 20.2454 5.984 3.38 0.0012Protein 5.69540 1.072 5.32 60.0001Fat 8.35958 1.033 8.09 60.0001Fiber -1.02018 0.4835 -2.11 0.0384Carbo 2.93570 0.2601 11.3 60.0001Sugars 3.31849 0.2501 13.3 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) To check the conditions, what plots of the data mightyou want to examine?d) What does the coefficient of Fat mean in this model?

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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.