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Simple Linear Regression: Correlation

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Wize University Statistics Textbook > Inference for Linear Regression

Simple Linear Regression Analysis

3 Activities

Wize University Statistics Textbook > Scatterplots, Association, and Correlation

Correlation

2 Activities

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.

2. If 𝒔𝒙 = 𝒔𝒚, then the slope cannot be less than – 𝟏 or greater than +𝟏.

3. If we double all the 𝒀 data and without changing the 𝑿 data, the correlation will not change but the slope will get steeper.

4. If the correlation between 𝑿 and 𝒀 is 𝒓 = 𝟏. 𝟎𝟎, then if 𝑿 increases by 60% then 𝒀 must increase by 60%.
More Simple Linear Regression Analysis Questions:
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
Linear Regression Analysis
The regression model y=4000−2.7xy=4000-2.7x is used to estimate the annual number of
cars going over the speed limit (y) based on the number of police officers on
the road. Estimate the number of cars going over the speed limit when there are
Linear Regression: Residual Plots
The equation y^=35+1.50x\hat{y}=35+1.50x is used to predict the hourly wage yy of someone with xx years of experience.
Elizabeth has 4 years of experience and earns $36 per hour. What is the residual?
Linear regression
Using the information provided below, solve for the slope and intercept of the linear regression equation.
∑x=702∑y=461∑xy=19,871∑x2=31396∑y2=13,449\begin{array}{ll}\sum x=702\\\sum y=461\\\sum xy=19,871\\\sum x^2=31396\\\sum y^2=13,449\end{array}
Linear regression
Savage question!
(iv) What body fat % would you predict for Mike who is turning 32 years old?
∑x=702∑y=461∑xy=19,871∑x2=31396∑y2=13,449\begin{array}{ll}\sum x=702\\\sum y=461\\\sum xy=19,871\\\sum x^2=31396\\\sum y^2=13,449\end{array}
Linear Regression Analysis
Suppose we want to see if there is a relationship between the size of a condo unit in Twin Pines and its selling price. We randomly sampled 32 units:
What is the explanatory variable (X)?
Simple Linear Regression Analysis
Given the information below, find the slope and intercept of the regression line. [Provide at least one decimal place, e.g. 8.2. Include negative sign if negative, e.g. -3.9.]
Linear Regression
Parts (a) to (c) are based on the following information.
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience. The correlation is r=0.56r=0.56. Suppose that xx is changed to months of experience.
(a) Which of the following will be the correct regression line?
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
Predictions and Residual Plots
The equation y^\hat{y}=35+1.50xx is used to predict the hourly wage yy of someone with xx years of experience.
(c) Elizabeth has 4 years of experience and earns $36. What is the residual?
Simple Linear Regression
Here is a residual plot for selling price (Y) vs. size of a condo in square-feet (X).
Which condition is violated?
More Correlation Questions:
The correlation between the number of hours of operation and sales in dollars at Pino's Pizza is 0.43. Which of the following is true?
Correlation and Regression Line
If r=−1.00r=-1.00, then 100% of the data points fall exactly on the regression line and the slope cannot be equal or greater than 0.
Correlation
The correlation between the number of hours of operation and sales in dollars at Pino's Pizza is 0.43. Which of the following is true?
Correlation
Numbers in a data set are in dollar units ($). 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.
Correlation: Coefficient of Determination
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.
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.