September, 29 2022

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Research Question

  • Does the temperature of the water and the age of the fish correlate with the length of a specific fish species?

  • The experiment was formed by taking a single species of fish , separating them into four tanks with four different temperatures, and measuring the fish every 14 days

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The Data
  • 44 Observations
  • I: Index
  • 2 variables
    • A1: the age of the fish (days)
    • A2: the water temperature (in degrees Celsius)
  • B: The length of the fish

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The Data
Length of Fish with Age and Water Temperature
Index Age WaterTemp Length
1 14 25 620
2 28 25 1315
3 41 25 2120
4 55 25 2600
5 69 25 3110
6 83 25 3535
7 97 25 3935
8 111 25 4465
9 125 25 4530
10 139 25 4570
11 153 25 4600
12 14 27 625
13 28 27 1215
14 41 27 2110
15 55 27 2805
16 69 27 3255
17 83 27 4015
18 97 27 4315
19 111 27 4495
20 125 27 4535
21 139 27 4600
22 153 27 4600
23 14 29 590
24 28 29 1305
25 41 29 2140
26 55 29 2890
27 69 29 3920
28 83 29 3920
29 97 29 4515
30 111 29 4520
31 125 29 4525
32 139 29 4565
33 153 29 4566
34 14 31 590
35 28 31 1205
36 41 31 1915
37 55 31 2140
38 69 31 2710
39 83 31 3020
40 97 31 3030
41 111 31 3040
42 125 31 3180
43 139 31 3257
44 153 31 3214

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Equation

B = A1 * X1 + A2 * X2

  • Multiple Linear regression

    • Variables water temperature and age

  • Regression Coefficients

    • A1 and A2

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The Residuals

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The Residuals Check for Normality

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The Output 
##               Estimate  Std. Error   t value     Pr(>|t|)
## (Intercept) 3904.26602 1149.044334  3.397838 1.522221e-03
## Age           26.24068    2.055093 12.768612 7.114144e-16
## WaterTemp   -106.41364   40.451824 -2.630626 1.195133e-02
  • The Estimate Coefficients:
    • For every one day increase in age, the length of the fish increases on average by about 26
    • For every degree Celsius increase in temperature, the average decrease in the length of the fish is 106
  • The P-value: The level of significance
    • The age p-value was HIGHLY significant, meaning there is a strong correlation between age and the length of the fish

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The Conclusion

  • The p-value shows that both variables are significant with the length of the fish

    • It can be concluded that as the fish grow older the length of the fish increases significantly

    • It can also be concluded fish that live in warmer temperatures are significantly smaller then those fish that live in cooler temperatures