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Correlation: Coefficient of Determination

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Wize University Statistics Textbook > Scatterplots, Association, and Correlation

Correlation

2 Activities

Wize University Statistics Textbook > Scatterplots, Association, and Correlation

Coefficient of Determination

3 Activities

True or false?

About 81% of the variation of quantities sold can be explained by price. The correlation between price and sales revenue is r=0.9r=0.9.


More Correlation Questions:
The correlation between the number of hours of operation and sales in dollars at Pino's Pizza is 0.43. Which of the following is true?
Correlation and Regression Line
If r=−1.00r=-1.00, then 100% of the data points fall exactly on the regression line and the slope cannot be equal or greater than 0.
Correlation
The correlation between the number of hours of operation and sales in dollars at Pino's Pizza is 0.43. Which of the following is true?
Correlation
Numbers in a data set are in dollar units ($). Which of the following measures will not be in dollar units?
Correlation
Which of the following statements is/or TURE? (select all that apply)
Correlation
True or False: A correlation coefficient of 0.6 means that 60% of the data points in the scatter plot have a linear relationship.
Predictions and Residual Plots
Suppose the following summary data was given:
x-variable: μx=10, sx=2\mu_x=10,\ s_x=2
y-variable: μy=250, sy=10\mu_y=250,\ s_y=10
Correlation
If we double all the YY data and without changing the XX data, the correlation will not change but the slope will get steeper.
Correlation
If R2=0.86R^2=0.86, then there must be a strong, positive correlation between XX and YY.
Correlation
The correlation between the number of hours of operation and sales in dollars at Pino's Pizza is 0.43. Which of the following is true?
Hypothesis Testing: Correlation
For the following statements, select true or false. Enter T for True, F for False.
Correlation
If we swap xx and yy, what will happen to the correlation coefficient rr?
Correlation
The correlation between midterm grades and final exam grades is r=0.88r=0.88. The correlation between assignment grades and final exam grades is r=0.44r=0.44.
Which of the following is false?
Correlation
In a plot, if we swap xx and yy, rr will not change.
Correlation
r>0r>0; large values of xx are associated with large values of yy.
Correlation
r=−0.91r=-0.91; the correlation is very weak.
Correlation
r<0r<0; increasing xx will cause yy to decrease.
Correlation
r=−1.00r=-1.00; the correlation is perfectly negative.
Correlation
r=2.00r=2.00; the correlation is very strong.
Correlation
r=0.33r=0.33; the correlation is positive, but weak.
Simple Linear Regression: Correlation
True or false? Enter T if True, F if False. (Use capital letters: T, F)
1. If 𝒓 = −𝟏. 𝟎𝟎, then 100% of the data points fall exactly on the regression line and the slope cannot be equal or greater than 0.
T
Correlation
The correlation is 0.56 when the unit for xx is years. What will the correlation coefficient be after xx is changed from years to months of experience? [Enter your answer with 2 decimal places, e.g. 0.36]
Correlation
Correlation rr has no units unless xx and yy have the same units.
More Coefficient of Determination Questions:
Coefficient of Determination
In a military aircraft the correlation between altitude (height) in feet (xx) and the number of hits (yy) on a certain target is 0.59. What is the correct conclusion?
Coefficient of Determination
In a military aircraft the correlation between altitude (height) in feet (xx) and the number of hits (yy) on a certain target is 0.59. What is the correct conclusion?
Coefficient of Determination
The following data is collected about 2 quantitative variables.
xˉ\bar{x}= 6 yˉ\bar{y}= 7
sxs_{x}= 2 sys_{y}= 2.6
Coefficient of Determination
(iii) What percent in the variation of body fat could be explained by age?
Coefficient of Determination
We want to see if the amount of training a employee receives is associated with the number of mistakes they make on the job. The coefficient of determination is 0.49.
True or false? Enter T for True; F for False.
Coefficient of determination
If the coefficient of determination r2r^2 is very strong, then xx and yy have a linear relationship.
Correlation and Residual Plots
Pamela and Tim are trying to be healthy by taking the stairs instead of the elevator. We want to see there is a relationship between the floor you live on and the time it takes to get to your floor from the lobby. Pamela lives on the 8th floor. Tim lives in the penthouse on the 20th floor.
∑x2=258\sum_{ }^{ }x^2=258
∑y2=687\sum_{ }^{ }y^2=687