Step 1 :Given the data of months and total employees, we are asked to find the slope of the best fit line. The slope of the line in this context represents the rate of change of the total number of employees with respect to time (months).
Step 2 :We can calculate the slope between each consecutive pair of points using the formula for the slope of a line, which is \((y2 - y1) / (x2 - x1)\).
Step 3 :Calculate the differences between consecutive months and employees: \[diff\_months = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\] \[diff\_employees = [1, 3, 3, 4, 5, 7, 7, 8, 12, 11, 14, 14]\]
Step 4 :Calculate the slopes between each consecutive pair of points: \[slopes = [1, 3, 3, 4, 5, 7, 7, 8, 12, 11, 14, 14]\]
Step 5 :Calculate the average slope by summing up all the slopes and dividing by the number of slopes: \[average\_slope = \frac{\sum slopes}{\text{number of slopes}} = \frac{1+3+3+4+5+7+7+8+12+11+14+14}{12} = 7.42\]
Step 6 :\(\boxed{\text{The predicted number of total employees in the company is increasing by approximately 7.42 for each increase in one month.}}\)