Question

Statistics students in Oxnard College sampled 11 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 (z) 201 Cost(y) 26.1 494 66.4 957 120.7 846 94.6 466 65.6 454 70.4 931 110.1 57.2 502 300 46 751 96.1 57.8 448 A student calculates a linear model (Please show your answers to two decimal places) Use the model to estimate the cost when number of pages is 361. (Please show your answer to 2 decimal places.) Cost $ License Points possible: 1 This is attempt 1 of 2. Submit

Answer 1

For the given sample

Sum of X = 6350
Sum of Y = 811
Mean X = 577.2727
Mean Y = 73.7273

Regression Equation = ŷ = bX + a

Now

X-MX Y - My -376.2727 -83.2727 379.7273 268.7273 - 111.2727 - 123.2727 353.7273 -75.2727 -277.2727 173.7273 - 129.2727 -47.6273 -7.3273 46.9727 20.8727 -8. 1273 -3.3273 36.3727 - 16.5273 7273 22.3727 - 15.9273 (X - MX)2 141581.1653 6934.3471 144192.8017 72214.3471 12381.6198 15196.1653 125122.9835 5665.9835 76880.1653 30181.1653 16711.438 (X-MX/Y - My) 17920.8438 610.162 17836.8256 5609.0711 904.3438 410.162 12866.0256 1244.0529 7688.0165 3886.7529 2058.962 - 27 SS: 647062. 1818 SP: 71035.2182

Sum of squares (SS_X) = 647062.1818
Sum of products (SP) = 71035.2182

Regression Equation = ŷ = bX + a

b = SP/SS_X = 71035.22/647062.18 = 0.10978

a = M_Y - bM_X = 73.73 - (0.11*577.27) = 10.35362

ŷ = 0.11X + 10.35

2. Let the cost is y hence at 361 pages

ŷ = 0.11X + 10.35

ŷ = 0.11*361 + 10.35

=50.06