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.
Question
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.
Solution
A. No, all the least-squares fit lines for these scatter plots do not necessarily have the same slope. The slope of the line depends on the relationship between the x and y variables in each individual data set.
B. No, all the least-squares fit lines do not necessarily have the same y-intercept. The y-intercept of the line depends on the specific values in the data set.
C. What all the least-squares fit lines have in common is that they are trying to minimize the sum of the squares of the residuals (the distances of the points from the line). This means they are all trying to best represent the relationship between the x and y variables in the data set.
D. When r is set to -0.90, all the least-squares fit lines for these scatter plots have in common that they show a strong negative correlation. This means that as x increases, y tends to decrease. The lines will slope downwards and the points will be close to the line, but not right on it.
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
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
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?
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?
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