Example 5: For the following data set: x 2 4 6...

Example 5: For the following data set: \begin{tabular}{|c|c|c|c|c|} \hline x & 2 & 4 & 6 & 8 \\ \hline y & 1 & 3 & 5 & 7 \\ \hline \end{tabular} (i) Find correlation coefficient ($r$). (ii) What is the relationship between the variables $x$ and $y$ (iii) Find the equation of regression line $y = mx + b$ (iv) Find the value of $y$ when $x = 5$

Transcript

00:01 Alright, so i see that you need help with this problem and it says compute the correlation coefficient between x and y for the following data and also regression lines so i know that i am using excel to do this however, you could use paper and pencil to do this.

00:17 You do not need a fancy program to answer this question excel i mean a paper pencil calculator a scientific calculator for function calculator will work just fine i will explain the process as i go in the event that you do have paper pencil and you do not have excel so that way but if you do have excel follow along because i can show you what how to do this or answer this problem so the first thing that i'm doing i'm just prepping it and you'll see why in a second because i'm gonna be highlighting the areas that of the values that i'm gonna end up using so the first thing that i'm gonna do is i'm gonna find the mean of x and to find the mean of x you add up all the values of your x values you divide by however many numbers there are and you get so this is my mean of x then i'm going to find the mean of y and mean of y then i'm going to take each one of my x values and i'm gonna subtract the mean of x so, let me just center all this so that means that i'm gonna take each one of these x values and subtract it from my mean of x so i'm gonna take 1 minus 5 .5 then i'm gonna do 2 minus 5 .5 and 3 minus 5 .5 so on and so forth then i'm going to do the same thing for y minus the mean of y.

01:57 I'm going to take 10 minus that's not right.

02:06 I found just the sum and not the average 30 .7.

02:14 So i'm going to take 10 minus 30 .7 then i'm gonna take this and drag it down because then i did 12 minus 30 .7 16 minus 30 .7 so on and so forth then i'm going to take x minus the mean of x and i'm going to multiply it by y minus the mean of y values...

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