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Published byBlaise Rice Modified over 9 years ago
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Once data is collected and organized, we need to analyze the strength of the relationship and formalize it with an equation By understanding the strength of the relationship, we can make estimates and predictions about the two variables being studied
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Graph with a few data points…
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Graph with a few more data points…
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Sometimes one data set will look more linear than another one There are varying degrees of linearity The more linear a set of data is, the closer the lines are to the line of best fit We use the CORRELATION COEFFICIENT to represent how far the points are on average from the line of best fit If r is close to +1 or -1, it’s a close fit The sign of r relates to the slope of the line, not the fit
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The following diagram illustrates how the correlation coefficient corresponds to the strength of a linear correlation: 1 0.67 0.33 0 -0.33 -0.67 Perfect Strong Moderate Weak None Weak Moderate Strong Perfect
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Sarah researches the cost of houses in a new area. She is looking for: A 2-storey, detached house Asking prices of $300,000 or less 2000 square feet of living space
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The following square footage with house prices were found in the neighbourhood of where Sarah was looking to buy a house: XY 1700271,900 1850289,900 1600277,900 1650289,900 1700279,000 1800294,900 1550269,900
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Draw the line that you think comes closest to matching the trend. Use the line to estimate how much a 2000 square foot house might cost in Sarah’s area.
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Sarah notices a new For Sale sign on a house in the area. At 2300 square feet and $384,500, it does not match her criteria. However, she decides to add the data to her collection anyway. Draw the new line of best fit Use this line to estimate the price for a 2000 square foot house in Sarah’s neighbourhood. Compare this estimate to your first estimate.
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XY 1700271,900 1850289,900 1600277,900 1650289,900 1700279,000 1800294,900 1550269,900 2300384,500
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How did the arrangement of plotted data affect the way you drew a line of best fit? How does it affect your confidence in using the line to make predictions? A real estate agent tells Sarah that 2000 square foot houses often come up for sale in this area, usually at prices from $295,000 to $305,000. How close were your estimates to these prices? Which line of best fit helped you make a closer prediction?
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What equation can we use to model the line of best fit? y = mx + b What does the y-intercept represent in this line of best fit? Does its meaning make sense in this context? Why or why not?
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Once you determine that two variables have a moderate to strong linear relationship, you can find a linear model. This way, you can make predictions for one variable based on the value of the other variable
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p. 175 #1, 2, 7, 9, 13
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