Find regression equation of the production when the capacity utilisation is 70%.productio mean 42 and standard deviation 12.5.capacity 88% and standard deviation 8.5.correlation coefficient 0.72?

To find the regression equation, we need to determine the relationship between the production and capacity utilization. The given information includes the mean, standard deviation, capacity, and correlation coefficient.

Let's denote the production as Y and the capacity utilization as X. The regression equation can be represented as:

Y = a + bX

Where:

Y = Production

X = Capacity Utilization

a = Y-intercept (constant term)

b = Slope of the regression line

To find the regression equation, we need to determine the values of a and b. The formula for calculating b (slope) is:

b = r * (Sy / Sx)

Where:

r = Correlation coefficient

Sy = Standard deviation of Y (Production)

Sx = Standard deviation of X (Capacity Utilization)

Given data:

Production mean (Ȳ) = 42

Production standard deviation (Sy) = 12.5

Capacity mean (X̄) = 0.88 (88%)

Capacity standard deviation (Sx) = 0.085 (8.5%)

Correlation coefficient (r) = 0.72

Now, we can calculate the slope (b):

b = 0.72 * (12.5 / 0.085)

b ≈ 106.47

Next, we can find the y-intercept (a) using the mean values:

Ȳ = a + bX̄

42 = a + (106.47 * 0.7)

42 = a + 74.529a = 42 - 74.529

a ≈ -32.529

Finally, we can write the regression equation:

Y = -32.529 + 106.47X

Therefore, the regression equation for the production when the capacity utilization is 70% is:

Production = -32.529 + 106.47 * Capacity Utilization