Correlation Coefficient
Find the correlation coefficient between List Price and each of the following variables.
• Bedrooms
• Baths-Total
• Stories d. Square footage
• Year Built f. Acreage
Answer 1:
The correlation coefficients of list price with other variables are as follows:
List Price | |
Bedrooms | 0.73 |
Baths - Total | 0.73 |
Stories | 0.24 |
Square Footage | 0.87 |
Year Built | 0.01 |
Acreage | 0.53 |
Interpreting Correlation Coefficient
For the variable in question 1 with the largest effect on List Price,
a. Interpret the correlation coefficient. (It must contain three key terms.)
b. Find the equation of the regression line.
c. Interpret the slope.
d. Draw the scatterplot with the regression line plotted.
e. Predict the List Price for the 25 th , 70th , and 78 th listed property.
f. Find the coefficient of determination.
g. Interpret the coefficient of determination. (Both percentages must be discussed.)
Answer2:
a) The value of correlation coefficient is largest for “square footage” at 0.87. Since the value is positive, it means that there exists a positive correlation between the two variables i.e. higher the square footage, higher is the list price and vice versa. And since the value is close to 1, it means that there is a strong relationship between the two variables. Since the value is greater than 0.87, this relationship is significant.
b) The equation for regression line can be written as:
List price = 3190.107 + 200.1043*Square footage
c) The value of slope is 200.1043 means that increase in the each unit square footage of a property results in about 200.1043 higher list price for the property and vice versa.
d) The scatter plot is as follows:
e) The square footage of
25th property is 3237 = 3190.107 + 200.1043*3237 = $650,927.7
70th property is 4433 = 3190.107 + 200.1043*4433 = $890,252.4
78th property is 2751 =3190.107 + 200.1043*2751 = $553,677
f) The value of coefficient of determination is 0.7552 (=0.869*0.869) and the value of adjusted R-sq is 0.7521.
g) The value of R-sq at 0.7552 tells that about 75.52% of the variation in the list price is explained by the square footage and the value of adjusted R-square is also very close at 75.21% because this is the only variable we have in the regression model.
Interpreting Y-intercept for a Variable
Only one of the variables in question 1 has a y-intercept that makes sense.
a. Which variable is it? Why?
b. Interpret the y-intercept for that variable.
Answer 3:
a) The y-intercept that would make sense is for variable “Baths – Total”. This makes sense as there can be a property with zero bathrooms but there will be other area for which the list price is computed.
b) The value of y-intercept of 2353.22 will mean that the average price of a property with zero bath rooms is $2,353.22.