Unable to come to same conclusion as text

Question

I am working through a problem using linear regression. The data set I have identified advertising as the x value, and sales as the y value. However, I am unable to calculate the Syx to the same result the text has been able to utilize the correct formula can you please review and advise how the text is calculating the solution?

Slope=109.229

Intercept=-8.135

r=.98

r2=.96

Syx=15.603

Answer 1

Note: Using Chart Information to Complete Linear Regression Question

Total X Sales = 8.2

Total Y Sales = 855

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Use a Simple Mathematics Method: Step by Step Approach

Step 1: Calculate the Sum of Products (Sxy) = x values times y values

1. Multiply each x value by its corresponding y value.
2. Sum up all these products.

2.5 (264) = 660

1.3(116) =150.8

1.4(165) = 231

1.0 x 101 = 101 example

2.0(209) =418

Total sum of Sxy = 1560.8

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Step 2: Calculate the Sum of Squares of x (Sxx) = x values times x values

1. Square each x value.
2. Sum up all these squared (x) values.

2.5^2 = 6.25, 1.3^2 = 1.69, 1.4^2 = 1.96, 1.0^2 = 1.0, and 2.0^2 = 4.0

Total sum of squares of x values (Sxx) = 14.9

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Step 3: Calculate the Mean of x and Mean of y:

1. Mean is the average of a set of numbers, calculated by summing all the numbers
2. Then dividing by the total count of numbers. 

x Mean = 8.2/5 = 1.64

x Mean = 1.64

y Mean = 855/5 = 171

y Mean = 171

Step 4: Calculate the Slope (b)

Sxy = 1560.8

Sxx = 14.9

b = Sxy divided by Sxx = 1560.8 divided by 14.9 = 104.75 = 105

Step 5: Calculate the y intercept (a)

ȳ= 171, x̄ = 1.64, b = 105

y intercept (a) = ȳ - (b times x̄) = 171 - (105 times 1.64) = -0.792751756 = - 0.79

a= - 0.79

Step 6: Regression Equation: y = a + bx

Substitute the calculated values of a and b into the equation: y = a + bx

y = - 0.79 + 105x

Solution: Linear Regression is y = - 0.79 + 105x

I hope this information is useful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H. 5/4/2025