Crowdly
Add to Chrome
This question is a hybrid question. Please clearly label a blank piece of pa...
✅ The verified answer to this question is available below. Our community-reviewed solutions help you understand the material better.
This question is a hybrid question. Please clearly label a blank piece of paper with this question number and write your response to this question.
(In the examination you may be required to take a photo of your response at the end of the examination to upload).
_____________________________________________________________________This question is worth 2 + 1 + 4 + 7 + 2 + 2 = 18 marks
[Note : This is an examination style REVISION question. In an actual examination question, there would not be as many parts]
In nature, the leaves of a certain variety of succulent plants are arranged in a spiral. [NB: The picture is for reference only]
Counting the number of leaves in the successive circles starting from the centre and moving outwards, the following number of leaves were counted.
Circle Number ( C )
|
1st
|
2nd
|
3rd
|
4th
|
5th
|
6th
|
7th
|
8th
|
9th
|
10th
|
Number of leaves ( N )
|
3
|
5
|
8
|
13
|
20
|
31
|
50
|
79
|
126
|
200
|
a. Find the value, correct to 2 decimal places,
of the correlation coefficient. What does this mean?
b. Use your graphics calculator to draw a residual plot. Briefly explain if a linear model is appropriate for this data set.c. Apply a squared transformationto transform the data.
i. Find the least square regression line for this transformation. [Give all coefficients to 2 decimal places]ii Find the correlation coefficient.iii. Is there any improvement? Why?
iv. Comment on the residual plot that is obtained with this transformation.d. Now apply a ) transformation to the original data set.i. Find the least square regression line for this transformation.
[Give all coefficients to 2 decimal places]
ii Find the correlation coefficient. [Give your answer to 4 decimal places]iii. Is there any improvement from the model in c.? Why?iv. Comment on the residual plot that is obtained with this transformation.v. Calculate, correct to 4 decimal places, the coefficient of determination. How
does this explain variation?
vi. Rewrite the equation in the form [Give all coefficients to 2 decimal places]e. Predict the number of leaves (to the nearest number) in the 11thcircle using the three different regression equations. How do they
compare with each other?
f. Find the residuals for the 7th circle using the three regression equations. Comment on your findings.