Statistics students in Oxnard College sampled 9 textbooks in the
Condor bookstore and recorded the number of pages in each textbook
and its cost. The bivariate data are shown below:
Number of Pages (xx) | Cost(yy) |
---|---|
347 | 42.29 |
714 | 77.98 |
576 | 54.32 |
485 | 52.95 |
397 | 53.79 |
828 | 69.96 |
333 | 42.31 |
891 | 81.37 |
615 | 66.05 |
A student calculates a linear model
y = ____ x + _____. (Please show your answers to two decimal
places)
Use the model to estimate the cost when number of pages is
426.
Cost = ____$ (Please show your answer to 2 decimal places.)
Solution:
X | Y | XY | X^2 | Y^2 |
347 | 42.29 | 14674.63 | 120409 | 1788.4441 |
714 | 77.98 | 55677.72 | 509796 | 6080.8804 |
576 | 54.32 | 31288.32 | 331776 | 2950.6624 |
485 | 52.95 | 25680.75 | 235225 | 2803.7025 |
397 | 53.79 | 21354.63 | 157609 | 2893.3641 |
828 | 69.96 | 57926.88 | 685584 | 4894.4016 |
333 | 42.31 | 14089.23 | 110889 | 1790.1361 |
891 | 81.37 | 72500.67 | 793881 | 6621.0769 |
615 | 66.05 | 40620.75 | 378225 | 4362.6025 |
n | 9 |
sum(XY) | 333813.58 |
sum(X) | 5186.00 |
sum(Y) | 541.02 |
sum(X^2) | 3323394.00 |
sum(Y^2) | 34185.27 |
Numerator | 198592.50 |
Denominator | 212445.46 |
r | 0.9348 |
r square | 0.8738 |
Xbar(mean) | 576.2222 |
Ybar(mean) | 60.1133 |
SD(X) | 169.9661 |
SD(Y) | 11.8604 |
b | 0.0658 |
a | 22.1706 |
Y hat = a + bX
= 22.17 + 0.07 X
Cost = 22.17 + 0.07 * 426
= $51.99
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