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 = slope of population regression line = .017 = y intercept of population regression line = -5.0 Houses in this community range in size from 1000 to 3000 square feet. a. What is the equation of the population regression line? b. Graph the population regression line by first finding the point on the line corresponding to x = 1000 and then the point corresponding to x = 2000, and drawing a line through these points. c. What is the mean value of gas usage for houses with 2100 sq. ft. of space? d. What is the average change in usage associated with a 1 sq. ft. increase in size? e. What is the average change in usage associated with a 100 sq. ft. increase in size? f. Would you use the model to predict mean usage for a 500 sq. ft. house? Why or why not?
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.
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 
= slope of population regression line = .017 
= y intercept of population regression line = -5.0 Houses in this community range in size from 1000 to 3000 square feet.
a. What is the equation of the population regression line?
b. Graph the population regression line by first finding the point on the line corresponding to x = 1000 and then the point corresponding to x = 2000, and drawing a line through these points.
c. What is the mean value of gas usage for houses with 2100 sq. ft. of space?
d. What is the average change in usage associated with a 1 sq. ft. increase in size?
e. What is the average change in usage associated with a 100 sq. ft. increase in size?
f. Would you use the model to predict mean usage for a 500 sq. ft. house? Why or why not?
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