Understanding Linear Regression and Correlation

What is the relationship between the distance from Times Square and hotel room cost according to the data collected by Steven?

• As distance increases, cost increases.

• As distance increases, cost decreases.

• Distance and cost are unrelated.

• Distance and cost both increase.

What is the first step in setting up the Desmos worksheet for this task?

• Label the axes.

• Enter the data into a table.

• Create a scatter plot.

• Generate a linear regression equation.

What is the significance of labeling the axes in the Desmos graph?

• It affects the correlation coefficient.

• It changes the slope of the line.

• It is not necessary for analysis.

• It helps in identifying the variables and their units.

Why is it important to ensure all data points are entered correctly in Desmos?

• Incorrect data points will not affect the analysis.

• Incorrect data points can lead to inaccurate calculations.

• It is not important as Desmos corrects errors automatically.

• It only affects the visualization, not the calculations.

What does the slope of the linear regression equation represent in this context?

• The cost of a hotel room at Times Square.

• The increase in cost per block closer to Times Square.

• The total cost of all hotel rooms.

• The decrease in cost per block further from Times Square.

What does the y-intercept of the linear regression equation indicate in this scenario?

• The distance from Times Square where cost is zero.

• The cost of a hotel room 20 blocks away.

• The cost of a hotel room at Times Square.

• The average cost of all hotel rooms.

How would you predict the cost of a hotel room 20 blocks away from Times Square using the linear regression equation?

• Divide the y-intercept by 20.

• Multiply the slope by 20 and add the y-intercept.

• Subtract 20 from the y-intercept.

• Add 20 to the y-intercept.

What is the correlation coefficient in this analysis, rounded to the nearest hundredth?

• -0.76

• 0.76

• 0.88

• -0.88

What does a strong negative correlation coefficient suggest about the relationship between distance and cost?

• Distance and cost both decrease.

• Distance and cost are unrelated.

• As distance increases, cost decreases.

• As distance increases, cost increases.

Which of the following best describes the correlation between distance from Times Square and hotel room cost?

• Strong positive correlation

• Weak positive correlation

• No correlation

• Strong negative correlation