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Using an Equation to Predict

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Direct deposit. The percentage of workers receiving direct
deposit of their paychecks went from 32% in 1994 to 60%
in 2004 (www.directdeposit.com). Let 1994 be year 0 and
2004 be year 10.

a) Write the equation of the line through (0, 32) and
(10, 60) to model the growth of direct deposit.

b) Use the accompanying graph to predict the year in
which 100% of all workers will receive direct deposit
of their paychecks.

c) Use the equation from part (a) to predict the year in
which 100% of all workers will receive direct deposit.

I have a very hard time with these, I just never seem to get the correct.

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Solution Preview


Lines have the equation y = mx + b. The "m" is the slope of the line, and the "b" is the y-intercept. Let's find the slope first:

m = (60 - 32)/(10 - 0) = 28/10 = 2.8

Now we know the line looks like y = 2.8x + b. Let's solve for b. Pick ...

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For the following data:
a) find the regression equation for the predicting y from x.
b) use the regression equation to find a predicted y for each x
c) find the difference between the actual y value and the predicted y value for each individual, square the differences and add the squared values to obtain ss residual.
d) calculate the Pearson Correlation for these data. Use r square and ssy to compute ss residual with equation 15.18.

x y
1 2
4 7
3 5
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5 14
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