Use a calculator to find the linear regression equation. Round to TWO decimal places for any decimals Profits (y) Years since 1995(x) (in thousands of dollars) 049 1 69 2 76 3 112 4 131 126
To find the linear regression equation, we need to calculate the slope and y-intercept.
Let's first calculate the mean of the profits and years since 1995:
Mean of profits (y):
(49 + 69 + 76 + 112 + 131) / 5 = 87.4
Mean of years since 1995 (x):
(1 + 2 + 3 + 4 + 5) / 5 = 3
Next, we calculate the slope (b) using the formula:
b = Σ((x - x̄)(y - ȳ)) / Σ(x - x̄)²
Substitute the values into the formula:
b = ((1-3)(49-87.4) + (2-3)(69-87.4) + (3-3)(76-87.4) + (4-3)(112-87.4) + (5-3)(131-87.4)) / ((1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²)
b = (-2 * -38.4 + -1 * -18.4 + 0 * -11.4 + 1 * 24.6 + 2 * 43.6) / (2² + 1² + 0² + 1² + 2²)
b = (76.8 + 18.4 + 0 + 24.6 + 87.2) / (4 + 1 + 0 + 1 + 4)
b = 207 / 10
b = 20.7
Now, we calculate the y-intercept (a) using the formula:
a = ȳ - b * x̄
Substitute the values into the formula:
a = 87.4 - 20.7 * 3
a = 87.4 - 62.1
a = 25.3
Therefore, our linear regression equation is:
y = 20.7x + 25.3
(The equation is y = 20.7x + 25.3)