(g) In order to perform a hypothesis test for a linear relationship between brai
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Question
(g) In order to perform a hypothesis test for a linear relationship between brain volume (cm3 ) and brain weight(g), we need four assumptions. They are
•independence of all pairs of observations (x1, y1),(x2, y2), . . .
• linear relationship between x and y
• constant variance of the residuals for all values of x
• normal distribution of the residuals for all values of x
Identify which plot(s) (A-D) on page 5 are used to verify these assumptions. Note that some plots can be used more than once. In all cases, make sure you can explain why or why not the assumption is met.
i. Linearity
A. Choose the plot(s) from the list that can be used to check the linearity assumption.
B. Is this assumption met? Yes / No
ii. Constant Variance
A. Choose the plot(s) from the list that can be used to check the constant variance assumption.
B. Is this assumption met? Yes / No
iii. Normality
A. Choose the plot(s) from the list that can be used to check the normality assumption.
B. Is this assumption met? Yes / No
iv. Independence
A. Choose the plot(s) from the list that can be used to check the independence assumption.
Plot (A) -Brain weight(g) 1000 1100 1200 1300 1400 1500 1600 Plot (B) Bivariate Fit of Brain weight(g) By Brain volume (cm^3) 1600 1500 1300 1100 2500 3000 500 5000 3500 Brain volume (cm 3 Plot (C) Residual by X Plot 250 150 100 50 100 150 200 3000 3500 4000 4500 Brain volume (cm 3) Plot (D) Residual Normal Quantile Plot 250 200 150 100 50 50 100 150 200 Normal QuantileExplanation / Answer
i Linearity
A. Plot B is used to check linearity.
B. Yes, this assumption is met. because scatter plot seems to follow the linear line and go in one direction.
ii Constant Variance
A. Plot C
B Yes this assumption is met. because scatter plot seems does have more or less same variation along the line and don't increase or decrease frantically.
iii. Normality
A. Both plot A and Plot D
B.Yes, this assumption is met. But the QQ plot(Plot D) shows a longer right tail. If the sample is small then this graph won't be of much help. Otherwise, it gives a good approximation to tell us that data is normal.
iv. Independence
A. Plot C
B Yes this assumption is met. because scatter plot seems does not seem to follow a series or fluctuating patterns around zero which would indicate that the error term was dependent.
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