Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found. The correlation coefficient is - 0.933
Determine R2 and interpret this statistic.
A) R2 = 93.3% which means that 93.3% of the variation in car price is explained by the age of the car.
B) R2 = 87.1% which means that 87.1% of the variation in car price is explained by the age of the car.
C) R2 = 93.3% which means that 93.3% of the variation in the age of the car is explained by the price of the car.
D) R2 = 87.1% which means that 87.1% of the variation in the age of the car is explained by the price of the car.
E) None of these are correct.
Is the answer C?
AND
The relationship between the number of games won during one season by a minor league baseball team and the average attendance at their home games is analyzed. A regression analysis to predict the average attendance from the number of games won gives the model
y-hat = -2600 + 222 wins
where y-hat is the predicted average attendance.
A team with 79 wins had a residual of 1562. What was the actual average attendance for this team?
Thanks in advance!!
I don't know about the second question, but the variation accounted for by a correlation coefficient is found by squaring the correlation coefficient.
For the first question:
The answer is A) R2 = 93.3% which means that 93.3% of the variation in car price is explained by the age of the car.
R2, or the coefficient of determination, is a measure of how well the regression model fits the data. It represents the proportion of the variance in the dependent variable (in this case, car price) that can be explained by the independent variable (age of the car).
In this case, an R2 value of 0.933 means that 93.3% of the variation in car price can be explained by the age of the car. This indicates a strong relationship between age and price, where the age of the car can explain almost all of the variation in car price.
For the second question:
To find the actual average attendance for the team with 79 wins, we can substitute the number of wins (79) into the regression model:
y-hat = -2600 + 222 * 79
y-hat = -2600 + 17438
y-hat ≈ 14838
Therefore, the actual average attendance for the team with 79 wins is approximately 14838.
To determine the correct answer for the first question about R2, we need to understand what R2 represents in the context of linear regression. R2, or the coefficient of determination, measures the proportion of the variation in the dependent variable (in this case, car price) that can be explained by the independent variable (car age). It ranges from 0% to 100%, where a higher value indicates a stronger relationship between the variables.
Given that the correlation coefficient is -0.933, we can square it to find R2. (-0.933)^2 = 0.8709, which is approximately 87.1%. Therefore, the correct answer is:
D) R2 = 87.1% which means that 87.1% of the variation in the age of the car is explained by the price of the car.
Now, let's move on to the second question about the actual average attendance for a team with 79 wins and a residual of 1562. In linear regression, the residual represents the difference between the actual observed value and the predicted value.
Given the regression model:
y-hat = -2600 + 222 wins
We can substitute the number of wins (79) into the equation to find the predicted average attendance:
y-hat = -2600 + 222 * 79
y-hat = -2600 + 17478
y-hat = 14878
The predicted average attendance is 14878. However, we are given a residual of 1562, which means the actual average attendance differs from the predicted value by this amount. By subtracting the residual from the predicted value, we can find the actual average attendance:
Actual average attendance = Predicted average attendance - Residual
Actual average attendance = 14878 - 1562
Actual average attendance = 13316
Therefore, the actual average attendance for the team with 79 wins is 13316.