3.7 Wild bears were caught and anesthetised so that various measurements could b
ID: 3070099 • Letter: 3
Question
3.7 Wild bears were caught and anesthetised so that various measurements could be made. The usefulness of a bear's chest circumference to predict its weight was of interest. A random sample of 10 bears was used, with the chest and weight measurements shown below, as well as the linear regression analysis. Bear Chest (inches) (pounds) 15 416 49 166 220 41 41 10 31 144 Model Std. Error Sig (Constant 251 948 33 814 CHEST 12.380 7451 810 983 15.277 a) b) c) d) State the linear regression equation. Can you interpret the meaning of the y-intercept in the context of this study? Explain. Interpret the slope of the regression equation in the context of these variables. Perform the hypothesis test for the slope and give your conclusion in words. 12+2+2+4 10 marks]Explanation / Answer
a) The linear regression equation is
Weight = -251.948 + 12.380 Chest
b) Y-Intercept = -251.948
If Chest of bear is zero inches then the weight of bear is -251.948 pounds which is meaning less
c) Slope = 12.380
which is positive value i.e. there is positive corrleation between chest and weight
i.e. as chest increase 1 inch, the weight is increased 12.380 pounds
d) H0: Slope(Beta1) is zero
H1: Slope (Beta1) is not zero
Test Statistic t = 15.277
P-value = 0.000 < alpha 0.05 so we reject H0
Thus we conclude that Slope (Beta1) is not zero
The regression equation is best fit to the given data
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