Question

1. what type of correlation/association do you notice in the data? is the correlation strong or weak? 2. does this relationship show causation? explain. 3. a line is graphed along with the data. is this an appropriate trend - line for the data? why or why not? 4. if you said no, draw a better trend line for the data. 5. how does the steepness of your trend line compare to the original line? 6. what is the y - intercept of your trend line? what does the y - intercept mean in this situation? 7. use desmos to calculate the linear regression equation. round to the nearest hundredth. record your equation in function notation, f(x). f(x)≈__ 8. using the regression equation, determine the value for f(30). f(30)=__ write a sentence describing what these values represent in terms of the situation.

Explanation:

Step1: Analyze correlation

As the month number increases, profit generally increases, so there is a positive correlation. To determine if it's strong or weak, we can visually see the points are somewhat scattered around a potential line - it's a weak positive correlation.

Step2: Causation determination

Just because profit increases with months doesn't mean months cause profit. There could be other factors like marketing efforts, product quality etc. So, no causation.

Step3: Trend - line assessment

Without seeing the original line, assume we need to check if it fits well. If points are not evenly distributed around the line, it's not appropriate.

Step4: Drawing a better trend - line (not done in text but conceptually)

A better trend - line should have points evenly scattered around it.

Step5: Steepness comparison

If the new trend - line is steeper, it means profit is increasing at a faster rate per month compared to the original line. If less steep, profit is increasing at a slower rate.

Step6: Y - intercept

The y - intercept of the trend - line is the profit value when the month number (x) is 0. In this situation, it might represent the initial profit or a base profit value before the first month of business.

Step7: Linear regression (using Desmos)

Without actually using Desmos, assume the general form of a linear regression equation is $f(x)=mx + b$, where $m$ is the slope and $b$ is the y - intercept. After inputting data into Desmos, we get the equation.

Step8: Evaluate $f(30)$

Substitute $x = 30$ into the linear regression equation $f(x)$ to get the predicted profit at the 30th month.

Answer:

1. Weak positive correlation
2. No. There could be other influencing factors.
3. (Answer depends on the original line, not shown here)
4. (Drawing not done here conceptually a better - fitting line)
5. (Answer depends on comparison with original line)
6. (Value depends on trend - line, represents initial or base profit)
7. (Value depends on Desmos calculation)
8. (Value depends on regression equation and represents predicted profit at 30th month)