00:01
So for part a here, it would appear that logically the independent variable is going to be the income.
00:16
We can also think of that as the explanatory variable, and then the dependent variable or response variable would be the food expenditure.
00:39
For part b, to draw a scatterplot for the above data, i've just used excel here.
00:43
The scatterplot should look something like this, so we can see that it does appear that there's a strong positive correlation.
00:51
For part c, finding the correlation coefficient r, i'll note that we find r by taking the sum of x minus x bar times y minus y bar, so that's the sum over all values of x and y minus their respective mean values, divided by the square root of the sum of x minus x bar squared times the sum of y minus y bar squared.
01:24
Now, since this is basically just going to involve a lot of tedious calculation, i've set up a excel spreadsheet here showing all the different steps that we would take.
01:34
So of course, first thing we do, find the averages.
01:36
These are the x bar and y bar values.
01:39
Then we go through and calculate x minus x bar times y minus y bar for each pair of x and y values.
01:45
Similarly, we find x minus x bar squared and y minus y bar squared.
01:49
And then adding up these columns gives us these three values, which we can then use.
01:53
To find our correlation coefficient.
01:55
So it's 211 .7143 divided by the square root of 801 .4286 times 60.
02:01
0 .85714...