4. There are different ways to find a line of best fit. The line of best fit fou

Question

4. There are different ways to find a line of best fit. The line of best fit found by the least squares method passes through the point (x,y ) where x x is the mean of the x-values of the data points (x, y) and y is the mean of the y-values. a. In MODE, change the number of fixed decimal places to 3. Use the data in the table below. Enter the number of teachers in L1. Enter the average salaries in L2. Find the LinReg line of best fit. (3 pts) Year 1999 2000 2001 2002 Techers (millions) 2.81 2.89 2.94 2.98 (thousands of dollars) 40.5 41.8 43.4 44.6 b Calculate x and y, the means for each data set. (To findx, for example, press 2nd STAT, Average Salary arrow over to MATH, then press 3 and enter L1.(4 pts) c·joraph the LinReg line of best fit. Select the CALC feature. Press 1, enter the value of X , and then press ENTER. Compare the y-value shown to y. What can you conclude? (2 pts) Critical Thinking Does (x,y ) lie on the LinReg line of best fit? From this result can you conclude that the LinReg line of best fit and the least squares line of best fit are the same? Are different? Explain. (2 pts) d.

Explanation / Answer

a)

As salary depend on number of teachers

The regression line of best fit is

y = 24.193x - 27.704

b)

x bar=2.905

y bar= 42.575

c)

y = 24.193*2.905 - 27.704=42.5767

Both the values are nearly equal y bar =42.575 and y hat=42.5767

d)

Yes x bar and y bar lies on the regression line hence both the lines are one and thesame

They are not different

As the difference between y hat that y bar is negligible hence we conclude that both the lines are same

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