King & Scott, a research firm for the real estate industry, studied the relation between x=x= annual income (in thousands of dollars) and y=y= sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table. Annual Income House Price 72 188 48 91.6 73 182.2 97 155.5 97 238.8 94 203.4 67 160.1 85 212 64 169 Conduct a linear regression. Use the results to answer the following questions. a. What is the value of the correlation coefficient (round to 3 decimal places)? What does the value tell you about the linear relationship between the annual income and the price of house purchased? Correlation coefficient: This indicates: very weak positive linear correlation fairly strong negative linear correlation perfect positive linear correlation very weak negative linear correlation perfect negative linear correlation no linear correlation fairly strong positive linear correlation b. What is the equation of the Least Squares line? Round the parameter values (slope and yy intercept) to 2 decimal places. ˆy=y^= c. If a buyer's annual income increases by $1000, the model's predicted change in DOLLARS of the sale price of the house they will purchase is: an of $
King & Scott, a research firm for the real estate industry, studied the relation between x=x= annual income (in thousands of dollars) and y=y= sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table.
| Annual Income | House Price |
|---|---|
| 72 | 188 |
| 48 | 91.6 |
| 73 | 182.2 |
| 97 | 155.5 |
| 97 | 238.8 |
| 94 | 203.4 |
| 67 | 160.1 |
| 85 | 212 |
| 64 | 169 |
Conduct a linear regression. Use the results to answer the following questions.
a. What is the value of the
Correlation coefficient:
This indicates:
- very weak
positive linear correlation - fairly strong
negative linear correlation - perfect positive linear correlation
- very weak negative linear correlation
- perfect negative linear correlation
- no linear correlation
- fairly strong positive linear correlation
b. What is the equation of the Least Squares line? Round the parameter values (slope and yy intercept) to 2 decimal places.
ˆy=y^=
c. If a buyer's annual income increases by $1000, the model's predicted change in DOLLARS of the sale price of the house they will purchase is:
an of $
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