Write a linear regression equation for a Full Service restaurant with the data 97; 118; 128; 140; 144; 147; 155. Fill in the correct answer for y = ________

Answer 1

To find the equation of a linear regression line, we need to find the slope (b) and the y-intercept (a).

First, we need the mean of the x-values (number of weeks, in this case) and the mean of the corresponding y-values (restaurant sales, in this case).

Let's calculate the mean of the x-values:
(97 + 118 + 128 + 140 + 144 + 147 + 155) / 7 = 125

Now, let's calculate the mean of the y-values:
(97 + 118 + 128 + 140 + 144 + 147 + 155) / 7 = 132

Next, we need to calculate the sum of the products of each x-value and y-value, and the sum of the squares of the x-values.

Sum of the products:
(97 * 97) + (118 * 118) + (128 * 128) + (140 * 140) + (144 * 144) + (147 * 147) + (155 * 155) = 155456

Sum of the squares of the x-values:
(97 * 97) + (118 * 118) + (128 * 128) + (140 * 140) + (144 * 144) + (147 * 147) + (155 * 155) = 16629

Now, let's calculate the slope (b):
b = (n * sum(xy) - sum(x) * sum(y)) / (n * sum(x^2) - (sum(x))^2)
b = (7 * 155456 - 7 * 125 * 132) / (7 * 16629 - (7 * 125)^2)
b = 2521 / 8694 ≈ 0.290

Finally, the y-intercept (a) can be calculated using the formula:
a = mean(y) - b * mean(x)
a = 132 - 0.290 * 125 = 132 - 36.25 ≈ 95.75

Therefore, the equation of the linear regression line is:
y = 0.290x + 95.75

So y = 0.290.

Answer 2

Now Type an expression using x as the variable use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed)

Answer 3

Certainly! Here's an expression using x as the variable:

5.678 * x + 3.214

Note: The coefficients in this expression are given as decimals rounded to the nearest thousandth.