DATA ANALYSIS:

I am going to determine whether or not the weight of an apple has any effect on it's circumference. I am going to get at least thirty apples (all apples being the same type) and take the weight of each apple individually. I will then take each apple and measure the circumference of each. ( Then these apples will then be turned into a pie :)). I believe that there will be a strong and positive association between the weight of an apple and it's circumference.

Here is the data that I collected:

Apple Circumference (in.) vs. Apple Weight (oz.)
Number of Apple
Apple Circumference (in.)
Apple Weight (oz.)
Number of Apple
Apple Circumference (in.)
Apple Weight (oz.)
Apple 1
9
5
Apple 16
8.938
5.1
Apple 2
8.624
4.55
Apple 17
8.562
4.9
Apple 3
8.562
5
Apple 18
8.25
4.15
Apple 4
8.686
5.15
Apple 19
9.062
5.75
Apple 5
8.374
4.5
Apple 20
8.438
5
Apple 6
8.5
4.75
Apple 21
8.662
5.1
Apple 7
8.624
4.25
Apple 22
8.186
4
Apple 8
8.124
4
Apple 23
8.186
4.15
Apple 9
8.562
4.5
Apple 24
8.374
4.25
Apple 10
8.5
4.2
Apple 25
8.5
4.3
Apple 11
8.75
5.2
Apple 26
8.374
5
Apple 12
8.438
5
Apple 27
7.75
3.75
Apple 13
8.438
4.5
Apple 28
8.186
4.25
Apple 14
8.32
4.45
Apple 29
8.374
4.9
Apple 15
8.32
4.5
Apple 30
8.374
4.3

PICTURE OF DATA COLLECTION:

Since I didn't have a flexible ruler nearby.....
Biometrika 2.jpg
I took a piece of paper and marked the circumference.
Biometrika 3.jpg
Then I placed the paper next to the measuring tape and recorded my circumference!
Biometrika 4.jpg

SCATTER PLOT:

Biometrika.PNG

CORRELATION:

Biometrika 5.PNG

r^2= .6193137224

Correlation of Determination:

r^2*100=61.93137224%


LEAST SQUARE REGRESSION EQUATION:

Biometrika 6.PNG

Least Square Regression Equation:

Circumference of Apple (in.) = 6.3318822 + .46284965 * Weight of an Apple (oz.)

Best Fitted Line Plot

Biometrika 7.PNG

RESIDUAL PLOT COMPARING X VALUES TO THE RESIDUALS


Biometrika 8.PNG

TRANSFORMATION OF RESIDUAL:

This residual I used was the reciprocal square root.
Screenshot 2017-11-21 at 8.07.28 AM.png

ANALYSIS OF RESULTS:

In my experiment, my goal was to see a strong and positive association between the weight of an apple to its circumference. Looking at my data and the correlation, .787, it shows a strong and positive association, indicating that there is some sort of relationship between the weight of an apple to its circumference. My normal residual graph had a small y-axis window of [-.3,.3], and that there was no pattern what so ever. This not only indicates a straight line, but a strong association. Then I graphed the transformation of the residual, which was the reciprocal square root, and that had a y-window of [-.005,.005], and again no pattern what so ever. This as well indicates not only a stronger straight line, but a very strong association too. This proves that there is some association between the weight of an apple, and it's circumference.

Some errors that could have occurred, was the measuring method that I used as well as the scale. I did not have a flexible ruler to measure out the circumference of the apple, which could have resulted in a miss-measurement. I also had a weight scale that wasn't the most precise measuring tool, which could again, result in a miss-measurement.