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   Â
   [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   Â
   [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]
=> Â [tex]b_o = 15.23[/tex]
  For a thickness of 1 cm  the predicted price is Â
   [tex]\= y = 15.23 + (3.625) *1[/tex]
  [tex]\= y =[/tex]  $18.86
