Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.013 ? = y-intercept of population regression line = −6 (a) What is the equation of the population regression line? y = (b) What is the mean value of gas usage for houses with 2200 sq. ft. of space? (c) What is the average change in usage associated with a 1 sq. ft. increase in size? (d) What is the average change in usage associated with a 100 sq. ft. increase in size?
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.
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Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values.
? = slope of population regression line = 0.013
? = y-intercept of population regression line = −6
(a) What is the equation of the population regression line?
y =
(b) What is the
(c) What is the average change in usage associated with a 1 sq. ft. increase in size?
(d) What is the average change in usage associated with a 100 sq. ft. increase in size?
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