INDIVIDUAL ASSIGNMENT 5:
REGRESSION & CORRELATION
– A CASE STUDY
Question 1
A biologist assumes that there is a linear relationship between the amount of
fertilizer supplied to tomato plants and the subsequent yield of tomato
obtained.
Eight tomato plants, of the same variety, were selected at random and
treated, weekly, with a solution in which x grams of fertilizer was dissolved in a
fixed quantity of water. The yield, y kilograms, of tomato was recorded.
(a) By using Data Analysis ToolPack in Microsoft Excel, shows the finding. (10
marks)
(b) State the equation of the least squares regression based on your finding.
(2 marks)
(c) Based on the findings, interpret the results, in-term of R square,
Significance F, coefficients and residuals. (20 marks)
(d) Estimate the yield of plant treated, weekly, with 3.2 grams of fertilizer. (2
marks)
(e) Indicate why it may not be appropriate to use your equation to predict the
yield of a plant treated, weekly, with 20 grams of fertilizer. (1 mark)
Plant A B C D E F G H
x 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
y 3.9 4.4 5.8 6.6 7.0 7.1 7.3 7.7
(a) Run regression analysis in Microsoft Excel to establish whether there
is a relationship between the variables. (Take a snapshot of the regression
result in your excel and past it in your report) (10 marks)
(b) State the equation of the least squares regression. (5 marks)
(c) Interpret the below of your regression analysis:
i. R square (5 marks)
ii. Significance F (5 marks)
iii. Coefficients (5 marks)
iv. Residuals (5 marks)
Umbrellas
Sold
Jan 82 15
Feb 92.5 25
Mar 83.2 17
Apr 97.7 28
May 131.9 41
Jun 141.3 47
Jul 165.4 50
Aug 140 46
Sep 126.7 37
Oct 97.8 22
Nov 86.2 20
Dec 99.6 30
Jan 87 14
Feb 97.5 27
Mar 88.2 14
Apr 102.7 30
May 123 43
Jun 146.3 49
Jul 160 49
Aug 145 44
Sep 131.7 39
Oct 118 36
Nov 91.2 20
Dec 104.6 32
Rainfall
(mm)
Question 2
Suppose weather channel management decides to develop a forecast model
for the average monthly rainfall based on the number of umbrellas sold over
the last 24 month. The Technical Officer collected data on rainfall and
umbrellas for 24 months. The following data show the umbrella sales and
rainfall recorded for 2019-2020.
Months
Question 3
Question 4
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