assignment 6a

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McMaster University *

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Business

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Apr 3, 2024

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Assignment 6a Ryan pollard 3661835 Question 1a To predict the lifespan of an animal with a certain length of gestation life span Y is used as a variable and for explanatory variable then gestation X is used as a variable Question 1b X y x2 y2 xy 8 30 64 900 240 2.1 12 4.41 144 25.2 1.3 6 1.69 36 7.8 1 3 1 9 3 11.5 25 132.25 625 287.5 5.3 12 28.09 144 63.6 3.8 10 14.44 100 38 24.3 40 590.49 1600 972 X57.3 y138 x2)2836.67 y2)3558 xy 1637.1 Question 1b Compute the correlation coefficient between the gestation period and the lifespan. Interpret the value. [4 marks] R= 8 x 1637.1 57.3 x 138 / √[ 8 x 836.37 – 57.3^2] x [ 8 x 3558 138 ^2] = 0.9159 Question1c c. At α = 0.05, can you conclude that there is a significant correlation between the two variables? [6 marks] ( Hint: Show the key steps of test of Hypothesis.)
H0: p =0 no correlation and Ho: p≠ 0 significant correlation Degree of freedom : 8-2 = 6 A=0.05 R= 0.9159 T = 0.9159 / √1 -(0.9159)^2/ 8-2 = 5.8591 Since t > critical value We reject the null hypothesis and conclude that there is significant correlation between the two Question 1d R^2 = 0.9159^2 = 0.83887 This means that 83.9% of the variability in y is explained by the model Question 1e There are other factors to consider in determining lifespan, such as genetics and Environment Question 1f Slope = M = 8 x 1637.1 57.3 x 138 / 8 x 836.37 57.3^2 = 1.52285 B = Σy – m Σx / n Intercept = B = 138 1.52285 x 57.3 / 8 = 6.3425 Question 1g Interpret the slope of the regression equation with reference to context. [2 marks] The slope is 1.523, this implies that an increase in gestation period by 1 unit increases the life span of the animal by 1.523 unit Question 1h =1.52285872752 (8) + 6.3425 = 18.5254 Residual 30 18.5254 = 11.47 Question 2a
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