Question

A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table below shows the data. (x) 0 10 20 30 40 50 60 70 80 90 (y) 2 52 102 152 202 252 302 352 402 452. Part A. Is there correlation between the number of workers in a factory and the number of units produced daily. Justify your answer. Part B. Write a function which best fits the data. Part C. What does the slope and y-intercept of the plot data indicate

Answer 1

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 $y=5 x+2$

Part C: The slope is $m=5$ which indicates the rate of change of number of units produced daily over the change in number of workers. The y - intercept is $b=2$ 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 $(0,2)$ and $(60,302)$ in the slope formula, to find the value of slope.

Hence, we have,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{302-2}{60-0}$

$m=\frac{300}{60}$

$m=5$

Thus, the slope is $m=5$

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 $x=0$, the value of y is 2

Hence, the y - intercept is $b=2$

Substituting the values $m=5$ and $b=2$ in the slope intercept form $y=m x+b$ , we get,

$y=5 x+2$

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 $m=5$ and y - intercept $b=2$

Substituting these values in the slope intercept form $y=m x+b$ , we get,

$y=5 x+2$

Thus, the function that best fits the data is $y=5 x+2$

Part C:

The slope is $m=5$

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 $b=2$

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

Learn more:

(1) Slope of a linear regression line is 1.5, and when x is 10 y takes the value of 8. determine the intercept of the regression line.

brainly.in/question/4802078

(2) Explain Linear Regression Equation.

brainly.in/question/9002335