Data are collected on the amount of fat (in grams) and calories in the french fry orders at nine fast food restaurants. The least-squares regression line for the data is \hat y =274.34+9.55xy^=274.34+9.55x, where \hat yy^ is the predicted number of calories and xx is grams of fat. Which of the following is the correct interpretation of the slope of the least-squares regression line?
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.
4. Data are collected on the amount of fat (in grams) and calories in the french fry orders at nine fast food restaurants. The least-squares regression line for the data is \hat y =274.34+9.55xy^=274.34+9.55x, where \hat yy^ is the predicted number of calories and xx is grams of fat. Which of the following is the correct interpretation of the slope of the least-squares regression line?
- (A) The calories increase by 9.55, on average.
- (B) For every increase in fat, the calories increase as well.
- (C) Every increase of 1 gram of fat causes an increase of 9.55 calories.
- (D) For every increase of 1 gram of fat, the predicted calories increase by 9.55.
- (E) For every increase of 1 calorie, the predicted grams of fat increase by 9.55.
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