In a study of housing demand, the county assessor is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor feels that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). He randomly selected 15 houses and measured both the selling price and size, as shown in the following table. OBSERVATIONi SELLING PRICE (× $1,000)Y SIZE (× 100 ft2 )X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 265.2 279.6 311.2 328.0 352.0 281.2 288.4 292.8 356.0 263.2 272.4 291.2 299.6 307.6 320.4 12.0 20.2 27.0 30.0 30.0 21.4 21.6 25.2 37.2 14.4 15.0 22.4 23.9 26.6 30.7 a. Plot the data.b. Determine the estimated regression line. Give an economic interpretation of the estimated slope (b) coefficient.c. Determine if size is a statistically significant variable in estimating selling price.d. Calculate the coefficient of determination.e. Perform an F-test of the overall significance of the results.f. Construct an approximate 95 percent prediction interval for the selling price of a house having an area (size) of 15 (hundred) square feet.
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.
In a study of housing demand, the county assessor is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor feels that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). He randomly selected 15 houses and measured both the selling price and size, as shown in the following table.
| OBSERVATION i |
SELLING PRICE (× $1,000) Y |
SIZE (× 100 ft2 ) X |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
265.2 279.6 311.2 328.0 352.0 281.2 288.4 292.8 356.0 263.2 272.4 291.2 299.6 307.6 320.4 |
12.0 20.2 27.0 30.0 30.0 21.4 21.6 25.2 37.2 14.4 15.0 22.4 23.9 26.6 30.7 |
a. Plot the data.
b. Determine the estimated regression line. Give an economic interpretation of the estimated slope (b) coefficient.
c. Determine if size is a statistically significant variable in estimating selling price.
d. Calculate the coefficient of determination.
e. Perform an F-test of the overall significance of the results.
f. Construct an approximate 95 percent prediction interval for the selling price of a house having an area (size) of 15 (hundred) square feet.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
