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Nata [24]
3 years ago
14

A lazy employee at an off-campus second-hand bookstore has decided that, rather than go searching through the book to find the c

orrect price, he will start pricing the books in relation to how thick they actually are. A sample of 10 books, ranging in thickness from 1 cm to 6 cm, gave the following results for thickness (x, in cm) and price (y, in $): Sxy = 87, Sxx = 24, Syy = 358.9, Σx = 30, and Σy = 261. What is the predicted price of a textbook that is 1 cm thick?
Mathematics
1 answer:
arsen [322]3 years ago
3 0

Answer:

The predicted price for  of a textbook that is 1 cm thick is \= y =   $18.86

Step-by-step explanation:

From the question we are told that

    The sample size is  n = 10

    The maximum thickness is t_{max} =  6 cm

     The minimum  thickness is t_{min} =  1 cm

       The sum  Σx = 30

        Sxy = 87

        Syy = 358.9

       Σy = 261

The mean thickness is

        \= x = \frac{\sum x}{n}

Substituting value

       \= x = \frac{30}{10}

       \= x = 3

The mean price of the book is

     \= y = \frac{\sum y}{n}

Substituting value      

     \= y = \frac{261}{10}

     \= y =26.1

Generally the least square regression equation is mathematically represented as

            \r  y = b_o + b_1 x

\r  y is the predicted price

Where  b_1  is a constant evaluated as

        b_o = \frac{SS_{xy}}{SS_{xx}}

Substituting value      

      b_o = \frac{87}{24}

      b_o = 3.625

At mean price and thickness The  least square regression equation becomes

          \= y = b_o + b_1 \= x

i.e  \r y = \= y , x= \= x

Substituting value

       26.1 = b_o + 3.625 * 3

=>   b_o =  15.23

   For a thickness of 1 cm  the predicted price is  

     \= y = 15.23 + (3.625) *1

    \= y =   $18.86

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