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Annual high temperatures in a certain location have been tracked for several years. Let
X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).

y=________
x=________

Annual high temperatures in a certain location have been tracked for several years Let X represent the year and Y the high temperature Based on the data shown b class=

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Answer:

Y= 19.86 - 0.42b

Step-by-step explanation:

Step 1: Write the formula

Regression Line: Y = a + bx

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

b= n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

Step 2: Make a table to find all values

X  Y          X^2    Y^2               XY

5 17.19 25 295.4961       85.95

6 19.12 36 365.5744       114.72

7 16.75 49 280.5625      117.25

8 15.58 64 242.7364       124.64

9 16.21 81 262.7641        145.89

10 14.14 100 199.9396        141.1

11 14.97 121 224.1009        164.67

12 16.2         144 262.44            194.4

68 130.16     620  2133.614       1088.62              TOTAL

Step 3: Substitute all values in the equation to find a and b

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

a= (130.16 x 620) - (68 x 1088.62)

                     8 x (620) - (68)^2

a = 80699.2 - 74026.16

                336

a = 19.86

b = n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

b = 8 x (1088.62) - (68 x 130.16)

             8 x (620) - (68)^2

b = 8708.96 - 8850.88

                336

b = -0.42

Step 4 : Apply values of a and b in the formula of the regression line.

Regression Line: Y = a + bx

Y= 19.86 + b (-0.42)

Y= 19.86 - 0.42b