I just need these answers checked, I did the math I just need someone to clarify. Thx

Question 1: The scatter plot shows the number of pumpkins that have been picked on the farm during October:

Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)

Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
My answer:
Part A: The correlation coefficient of r = 0.51 is accurate based on the scatter plot.

Also, the farther the data points are from each other along the trendline, the farther the correlation coefficient, r, is from 1 or -1. If they are moderately apart, the correlation coefficient would be around 0.5/-0.5 and 0.65/-0.65, as the case may be.

Part B: A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.
Question 2:
A manager is assessing the correlation between the number of employees in a plant and the number of products produced yearly. The table shows the data:

Number of employees
(x) 0 25 50 75 100 125 150 175 200
Number of products
(y) 10 160 310 460 610 760 910 1060 1210
Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly? 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)

My answer:
Part A: Yes, there is a clear correlation between the number of employees working in the plant and the number of products produced, as indicated by the table provided. Specifically, as the number of employees increases from 0 to 200, the number of products produced increases from 10 to 1,260 per year. This suggests that an increase in the number of employees leads to an increase in production output.

Part B:




Function: y = 6x + 10.




The constant difference between the number of products produced is 150.

The following information pertains to the line connecting the first and last data points:

The slope is calculated as follows:

The y-intercept represents the number of products produced when the number of employees is 0, and it is 10.

Therefore, the data follows a linear function, and the equation for the line is as follows:

y = 6x + 10

Where:

- y represents the number of products produced yearly

- x represents the number of employees in the factory.

Part C:

The slope of the line represents the production rate of each employee, with a value of 150 units per year. The intercept of the line is 10 units of products when there are no employees.