Questions: After reviewing my data set from week 2, I've right clicked on my trendline to open more options. I then selected format trendline to open the format trendline options. Once that was opened, I've checked the display equation on chart box and the display R-squared value on chart. After reviewing my R-squared value, I need to find R. I then put the value of my R-squared 0.3659 in my calculator and pressed the square root button to get ( 0.605 ). Finding the correlation coefficient ( R ) allows me to determine if my regression is positive, negative, or neither on a -1,0,1 scale. By having an R=0.605, it's closer to the 1 value giving it a strong correlation. It makes sense. When I first completed my scatter plot it already showed an upward trend meaning it is positive. The 10 -yeas r-old boys were pretty close to the trendline proving it's strength. Honestly, at first all I had was the graph and trendline to show what's already shown. Now, with having a number tied to the correlation allows me to compare it even better. You can even make it into a percentage 100% through -100%. So, if I were to make mine into a percentage it will give me 60%. The strength of the correlation of Y being the weight in pounds and X being the height in inches correlate to 60%. I'm interested to learn and see what else we can do. What more information can we pull from the value already given?

After reviewing my data set from week 2, I've right clicked on my trendline to open more options. I then selected format trendline to open the format trendline options. Once that was opened, I've checked the display equation on chart box and the display R-squared value on chart. After reviewing my R-squared value, I need to find R. I then put the value of my R-squared 0.3659 in my calculator and pressed the square root button to get ( 0.605 ). Finding the correlation coefficient ( R ) allows me to determine if my regression is positive, negative, or neither on a -1,0,1 scale. By having an R=0.605, it's closer to the 1 value giving it a strong correlation. It makes sense. When I first completed my scatter plot it already showed an upward trend meaning it is positive. The 10 -yeas r-old boys were pretty close to the trendline proving it's strength. Honestly, at first all I had was the graph and trendline to show what's already shown. Now, with having a number tied to the correlation allows me to compare it even better. You can even make it into a percentage 100% through -100%. So, if I were to make mine into a percentage it will give me 60%. The strength of the correlation of Y being the weight in pounds and X being the height in inches correlate to 60%. I'm interested to learn and see what else we can do. What more information can we pull from the value already given?
Transcript text: After reviewing my data set from week 2, I've right clicked on my trendline to open more options. I then selected format trendline to open the format trendline options. Once that was opened, I've checked the display equation on chart box and the display $R$-squared value on chart. After reviewing my $R$-squared value, I need to find $R$. I then put the value of my R-squared 0.3659 in my calculator and pressed the square root button to get ( 0.605 ). Finding the correlation coefficient ( $R$ ) allows me to determine if my regression is positive, negative, or neither on a $-1,0,1$ scale. By having an $R=0.605$, it's closer to the 1 value giving it a strong correlation. It makes sense. When I first completed my scatter plot it already showed an upward trend meaning it is positive. The 10 -yeas r-old boys were pretty close to the trendline proving it's strength. Honestly, at first all I had was the graph and trendline to show what's already shown. Now, with having a number tied to the correlation allows me to compare it even better. You can even make it into a percentage 100\% through $-100 \%$. So, if I were to make mine into a percentage it will give me $60 \%$. The strength of the correlation of $Y$ being the weight in pounds and $X$ being the height in inches correlate to $60 \%$. I'm interested to learn and see what else we can do. What more information can we pull from the value already given?
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Solution

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Solution Steps

To find the correlation coefficient \( R \) from the given \( R^2 \) value, you simply need to take the square root of \( R^2 \). This will give you the absolute value of \( R \). Since the context of the problem suggests a positive correlation (as indicated by the upward trend in the scatter plot), \( R \) will be positive.

Step 1: Identify the Given Value

The problem provides the value of \( R^2 = 0.3659 \).

Step 2: Calculate the Correlation Coefficient

To find the correlation coefficient \( R \), take the square root of \( R^2 \): \[ R = \sqrt{0.3659} \approx 0.6049 \]

Step 3: Interpret the Correlation Coefficient

The value of \( R = 0.6049 \) indicates a moderate positive correlation between the variables, as it is closer to 1 than to 0.

Final Answer

\(\boxed{R = 0.6049}\)

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