Explanation:
We are given a table of x and y values along with other information that is useful to calculate the regression equation that models the data.
Step 1. The equation will have the following form:
[tex]y=mx+b[/tex]
Where m is the slope of the line, and b is the y-intercept of the line.
Step 2. There are two formulas useful to calculate m and b, and they are presented in the following image:
Where the symbol
∑
represents a summation.
The summations are already presented in the table:
We will use the values to substitute in our formulas.
Step 3. In our formulas, there is a value 'n', this value represents the number of elements in the data, in this case, n is equal to 5:
[tex]n=5[/tex]
Substituting the values from the table and the value of n to find m:
[tex]m=\frac{(5)(693.75)-(23.25)(127)}{(5)(129.56)-(23.25^)^2}[/tex]
Solving the operations, we find the value of m:
[tex]m=4.8117[/tex]
We can round this value to
[tex]m=4.8[/tex]
Step 4. We already have m, so now we need to find b:
Substituting the known values:
[tex]b=\frac{127-4.8(23.25)}{5}[/tex]
Solving the operations:
[tex]b=3.08[/tex]
we can round this to
[tex]b=3[/tex]
Step 5. Remember that our equation has the form
[tex]y=mx+b[/tex]
The last step is to substitute our m and b values:
[tex]y=4.8x+3[/tex]
And we have found the line equation which is the first option.
Answer:
[tex]y=4.8x+3[/tex]
