Determining Linear Regression Equations and Correlation Coefficients

This video tutorial covers the basics of linear regression, focusing on determining linear regression equations and correlation coefficients. It explains the concept of correlation coefficient, also known as the r value, and its role in assessing data fit. The tutorial includes two example problems: predicting attendance at a football game and a spring concert, using Desmos for calculations. The video emphasizes the importance of rounding and interpreting results for data prediction.

What is the range of values for the correlation coefficient?

• 0 to 1

• -1 to 1

• -1 to 0

• 0 to 2

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If the correlation coefficient is between 0 and 1, what does it indicate?

• Positive association

• Weak association

• Negative association

• No association

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CCSS.HSS.ID.B.5

What should you do before starting to input data into Desmos?

• Calculate the correlation coefficient manually

• Change the pin color

• Pause the video and load Desmos

• Write down the data set

Which symbol is used in Desmos to represent the regression equation?

• y1 ~ ax1 + b

• y = mx + b

• y ~ mx + b

• y1 = ax1 + b

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How do you input a subscript in Desmos?

• Press the tilde button

• Use the ABC keyboard option

• Hold shift and press the minus button

• Hold shift and press the plus button

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CCSS.HSF-IF.C.7A

What is the correlation coefficient if the r value is 0.97?

• 1.0

• 0.5

• 0.7

• 0.97

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CCSS.HSF-LE.A.1B

What does an r value of 0.97 indicate about the fit of the data?

• Poor fit

• No fit

• Moderate fit

• Good fit

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How do you predict the attendance for game nine using the linear regression equation?

• Add 9 to the correlation coefficient

• Replace x with 9 in the equation

• Replace y with 9 in the equation

• Multiply the correlation coefficient by 9

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When dealing with years in a data set, what should you convert them into?

• Single digits

• Weeks

• Months

• Days

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What is the predicted attendance for the year 2017 in the spring concert data set?

• 2000

• 771

• 250

• 1021