PLS HELP A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table shows the data: Number of workers
(x) 0 10 20 30 40 50 60 70 80 90
Number of units
(y) 2 52 102 152 202 252 302 352 402 452

Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)

Part B: Write a function that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Part A: Yes. There is a correlation between the number of workers in a factory and the number of units produced daily.

Part B: The equation of the function that best fits the data is

Part C: The slope is  which indicates the rate of change of number of units produced daily over the change in number of workers. The y - intercept is  which indicates the number of units produced by number of workers.

Explanation:

Part A: To determine the correlation coefficient, first we shall find the slope and y - intercept.

Let us substitute the coordinates  and  in the slope formula, to find the value of slope.

Hence, we have,

Thus, the slope is

The y - intercept is the value of y when the value of x is equal to 0.

Thus, from the table , we can see that when , the value of y is 2

Hence, the y - intercept is

Substituting the values  and  in the slope intercept form  , we get,

Hence, there is a linear correlation between the number of workers in a factory and the number of units produced daily.

Part B: To find the function that best fits the data, let us substitute the value of slope and y - intercept in the slope intercept formula.

Since, we have already found slope  and y - intercept

Substituting these values in the slope intercept form  , we get,

Thus, the function that best fits the data is

Part C:

The slope is

The slope indicates that the rate of change of number of units produced daily over the change in number of workers.

The y - intercept is

The y - intercept indicates that the number of units produced by number of workers.

Step-by-step explanation:

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