D. Set r to –0.90. Click Same r several times. What do the least-squares fit lines forthese scatter plots have in common?A negative r indicates a negative correlation: as x increases, y tends to decrease
Question
D. Set r to –0.90. Click Same r several times. What do the least-squares fit lines forthese scatter plots have in common?A negative r indicates a negative correlation: as x increases, y tends to decrease
Solution
The question seems to be asking about the common characteristics of least-squares fit lines for scatter plots when the correlation coefficient (r) is set to -0.90.
Here's a step-by-step answer:
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The correlation coefficient, r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1. A value of -0.90 indicates a strong negative correlation.
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When you set r to -0.90 and generate several scatter plots, each plot will show a different set of data points but the overall trend will be the same: as the x-values increase, the y-values tend to decrease. This is what a negative correlation means.
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The least-squares fit line, also known as the line of best fit, is a straight line that best represents the data on a scatter plot. For each scatter plot you generate with r set to -0.90, the line of best fit will slope downwards, reflecting the negative correlation.
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Despite the different data points on each scatter plot, the lines of best fit will all have a similar steepness or slope. This is because the slope of the line of best fit is determined by the correlation coefficient, which is the same (-0.90) for all the scatter plots.
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In conclusion, the least-squares fit lines for these scatter plots will all show a strong negative correlation, as indicated by their downward slope. The exact position and data points of each line may vary, but the overall trend will be the same.
Similar Questions
3. Set r to 0.00. Click Same r several times.A. Do all the least-squares fit lines for these scatter plots have the same slope?B. Do all the least-squares fit lines have the same y-intercept?C. What do all the least-squares fit lines have in common?When r = 0, there is no correlation in the data. This means that the value of y doesnot seem to be at all related to the value of x
With Show least-squares fit line still selected, set r to 0.90. The points should be close tothe line, but not right on it. Below Generate new data set with: click Same r several times.A. Do all the least-squares fit lines for these scatter plots have the same slope?B. Do all the least-squares fit lines have the same y-intercept?C. What do all the least-squares fit lines have in common?A positive r indicates a positive correlation: as x increases, y also tends to increase.D. Set r to –0.90. Click Same r several times. What do the least-squares fit lines forthese scatter plots have in common?A negative r indicates a negative correlation: as x increases, y tends to decrease.
What do all the least-squares fit lines have in common?When r = 0, there is no correlation in the data. This means that the value of y doesnot seem to be at all related to the value of x
1. In a data set with a strong linear correlation, the points in the scatter plot approximate a line.Turn on Show least-squares fit line. The least-squares fit line is the “best-fit” line, or theline that most closely “fits” the shape of the data.A. When r = 1, how are the points in the scatter plot related to the least-squares fit line?B. Slowly decrease r. How does this affect where the points are in relation to the line?
Activity:Correlation andlines of best fitGet the Gizmo ready: Set r to 1.00. (To quickly set a slider to a specificvalue, type the value into the text box to the rightof the slider, and hit Enter.)1. In a data set with a strong linear correlation, the points in the scatter plot approximate a line.Turn on Show least-squares fit line. The least-squares fit line is the “best-fit” line, or theline that most closely “fits” the shape of the data.A. When r = 1, how are the points in the scatter plot related to the least-squares fit line?B. Slowly decrease r. How does this affect where the points are in relation to the line?2. With Show least-squares fit line still selected, set r to 0.90. The points should be close tothe line, but not right on it. Below Generate new data set with: click Same r several times.A. Do all the least-squares fit lines for these scatter plots have the same slope?B. Do all the least-squares fit lines have the same y-intercept?C. What do all the least-squares fit lines have in common?A positive r indicates a positive correlation: as x increases, y also tends to increase.D. Set r to –0.90. Click Same r several times. What do the least-squares fit lines forthese scatter plots have in common?A negative r indicates a negative correlation: as x increases, y tends to decrease.3. Set r to 0.00. Click Same r several times.A. Do all the least-squares fit lines for these scatter plots have the same slope?B. Do all the least-squares fit lines have the same y-intercept?C. What do all the least-squares fit lines have in common?When r = 0, there is no correlation in the data. This means that the value of y doesnot seem to be at all related to the value of x.(Activity continued on next page)Activity (continued from previous page)4. Turn off Show least-squares fit line. Click New r, andsketch the scatter plot to the right.What is the value of r?Turn on Fit a line. Use the slope (m) and y-intercept (b)sliders to estimate the line that fits this data set best.Sketch your line and record its equation below.Equation of estimated line:Check your estimate by turning on Show least-squares fit line. Record the equation for theactual least-squares fit line.Least-squares fit line equation: Was your estimate close?5. Turn off Show least-squares fit line. Click New r several times. For each data set, try to fitthe red line to the data, and then check it by turning on Show least-squares fit line.How does the value of r relate to how easy it is to estimate the least-squares fit line?
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