Vocabulary: correlation, correlation coefficient, least-squares fit line, scatter plotPrior Knowledge Questions (Do these BEFORE usingthe Gizmo.)Mr. Bryant asks his students how far they live from school,and their travel time to get to school. He plots a point foreach student’s distance in miles (x) and travel time inminutes (y) to create a scatter plot of his data.1. Suppose Mr. Bryant’s student Elena lives 3 miles fromschool and it takes her 15 minutes to get to school.What point will Mr. Bryant plot for Elena? ( , )2. How do you think increased distance will affect travel time?3. Sketch points in the grid above to illustrate what you think the data might look like
Question
Vocabulary: correlation, correlation coefficient, least-squares fit line, scatter plotPrior Knowledge Questions (Do these BEFORE usingthe Gizmo.)Mr. Bryant asks his students how far they live from school,and their travel time to get to school. He plots a point foreach student’s distance in miles (x) and travel time inminutes (y) to create a scatter plot of his data.1. Suppose Mr. Bryant’s student Elena lives 3 miles fromschool and it takes her 15 minutes to get to school.What point will Mr. Bryant plot for Elena? ( , )2. How do you think increased distance will affect travel time?3. Sketch points in the grid above to illustrate what you think the data might look like
Solution
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Mr. Bryant will plot the point (3, 15) for Elena. This is because she lives 3 miles from school (which is the x-coordinate) and it takes her 15 minutes to get to school (which is the y-coordinate).
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Generally, an increased distance would likely increase the travel time. This is because the further away something is, the longer it usually takes to get there. However, this can also depend on other factors such as traffic, speed, and mode of transportation.
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Without specific data points, it's hard to sketch an accurate scatter plot. However, based on the assumption that increased distance increases travel time, the points would likely form an upward trend. This means that as the x-values (distance) increase, the y-values (travel time) also increase. The points might be scattered around, but they would generally follow this upward trend. This could be represented by a least-squares fit line, which is a line that best fits the data points on the scatter plot.
The correlation between the two variables (distance and travel time) can be measured using the correlation coefficient. This is a statistical measure that calculates the strength of the relationship between the relative movements of the two variables. The correlation coefficient ranges from -1 to 1. A correlation of 1 indicates a perfect positive correlation, meaning that both variables move in the same direction together. In this case, if the correlation coefficient is close to 1, it would mean that as the distance from school increases, the travel time also increases.
Similar Questions
The scatter plot shows the number of hours worked and money spent on entertainment by each of 21 students. Also shown is the line of best fit for the data.Fill in the blanks below.y510152025303540455055606570x2468101214161820220AmountofmoneyspentonentertainmentindollarsNumberofhoursworked(a)For these 21 students, as the number of hours increases, the amount of money spent tends to ▼(Choose one)(b)For these 21 students, there is ▼(Choose one) correlation between the number of hours worked and the amount of money spent.(c)Using the line of best fit, we would predict that a student working 12 hours would spend approximately ▼(Choose one)
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?
16. Scatter diagrams are useful to learn … the X and Y variables have high or low correlations.1 poina. wetterb. wetherc. weatherd. whether
If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:Group of answer choices–1.0.0.0. 1.0.either 1.0 or –1.0.Next
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