Answer:
The predicted price for of a textbook that is 1 cm thick is [tex]\= y =[/tex] $18.86
Step-by-step explanation:
From the question we are told that
The sample size is n = 10
The maximum thickness is [tex]t_{max} = 6 cm[/tex]
The minimum thickness is [tex]t_{min} = 1 cm[/tex]
The sum Σx = 30
Sxy = 87
Syy = 358.9
Σy = 261
The mean thickness is
[tex]\= x = \frac{\sum x}{n}[/tex]
Substituting value
[tex]\= x = \frac{30}{10}[/tex]
[tex]\= x = 3[/tex]
The mean price of the book is
[tex]\= y = \frac{\sum y}{n}[/tex]
Substituting value
[tex]\= y = \frac{261}{10}[/tex]
[tex]\= y =26.1[/tex]
Generally the least square regression equation is mathematically represented as
[tex]\r y = b_o + b_1 x[/tex]
[tex]\r y[/tex] is the predicted price
Where [tex]b_1[/tex] is a constant evaluated as
[tex]b_o = \frac{SS_{xy}}{SS_{xx}}[/tex]
Substituting value
[tex]b_o = \frac{87}{24}[/tex]
[tex]b_o = 3.625[/tex]
At mean price and thickness The least square regression equation becomes
[tex]\= y = b_o + b_1 \= x[/tex]
i.e [tex]\r y = \= y , x= \= x[/tex]
Substituting value
[tex]26.1 = b_o + 3.625 * 3[/tex]
=> [tex]b_o = 15.23[/tex]
For a thickness of 1 cm the predicted price is
[tex]\= y = 15.23 + (3.625) *1[/tex]
[tex]\= y =[/tex] $18.86
