QUESTION 32 State whether you think that the variables have strone correlation, weak negative correlation; Joritiye correlatlon: weak posltive correlation_ no comel...

In Exercises $39-44,$ plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of $r$ and confirm your result. The number $r$ is called the correlation confficient. It is a measure of how well the model fits the data. Correlation coefficients vary between $-1$ and $1,$ and the closer $|r|$ is to $1,$ the better the model. (GRAPH NOT COPY) Positive correlation Negative correlation No correlation $$ (1,4),(2,6),(3,8),(4,11),(5,13),(6,15) $$

Given the set of six data points and I plotted them here and we can see that basically there looks to be no trend. So I would say there's absolutely no correlation here. I can't see any general trend whatsoever. And in fact, if we were to to plot a, if we look at the linear regression, we see that the slope is actually basically zero. So then the linear regression, we see that we have the slope of zero, which means that there's really absolutely no correlation that we can find here and then r squared are are obviously zero. To know if we put a trendline on here. Let's see. You try to put a linear trend. We can see here and we have our square value that the best we can do what the line is. Say that it's constant. It's a roughly four. Okay, so it's basically the average of all these points is for having a C r squared zero. Basically, you know, the trend. There is no correlation here. and basically we can't do anything. I mean obviously if you did a higher order fit, so say you used the polynomial, you know, quadratic is okay cubic, You know, not so great. Then a core tech. And then Quinn tick actually will Because there's six data points and there's 1, 2, 3, 4, 5, 6 constants in this. You see that r squared is one because um with six data points and six constants we can make sure that the function goes through all the data points. So obviously as we go down, you can see that R squared, even a cubic does a really poor job. Quadratic is terrible and linear. We have to actually change this back to linear. Does basically the worst that you could possibly do with the r squared value of zero.

In this question. We have a correlation coefficients, and you have to classify it. Okay, so you have to classify it. I see that strong, positive, moderate, positive. None. Moderates. Negative or strong Negative. The correlation coefficients. Given this 0.3 so are is equal to 0.3. Therefore the cracks And so I fear, should be moderate. Positive? No, Give a short explanation off. Why? Although the value off our Ismael, it's not very close to sue. Also, our is positive.

The simple answer here is no. And let me give you the explanation. A correlation coefficients off. Negative one indicates this perfect linear relationship between I prefer to linear relationship between the data values while US a coalition coefficient off zero zoo in the off zero indicates no linear relationship as this between the data values.

In this question. We have a correlation coefficients, and you have to classify it. Okay, so you have to classify it. I see that strong, positive, moderate, positive. None. Moderates negative or strong negative. The correlation coefficients given to us zero so are is equal to zoo. And when the correlation coefficient is is you, we know that this new linear relationship therefore the correct option here for us to choose will be none between the kids that they snore linear relationship between the fire Abu's or between the data values.