3. Brain Weight and its Volume The file called brain.jmp contains data on the vo

Question

3. Brain Weight and its Volume The file called brain.jmp contains data on the volume of 237 human brains, as well as its corresponding weight (). We want to predict the brain weight(g) based on the brain volume (m). (a) Free Response.] Identify the Explanatory and Response Variables. Make sure you use exact wording from problem statement. (b) Fit a least squares regression model to the data in JMP) through the commands Analyze Fit Y by X, correctly casting the variables into their roles of "Y" and "X" Then select Fit Line from the "red triangle" menu. Using the output, report: i. The value of the sample intercept b. Round to four decimal places. ii. The value of the sample slope b. Round to four decimal places. (c) Free Response.] Interpret the sample slope bi within the context of the problem. (d) A person has a brain volume of 3478 cm23 Predict the brain weight of the person using the (e) Assume that the predicted brain weight from 3d was 1240 g. Mr. A has a brain volume of (f) Free Response.] Based on the residual from 3e, was Mr. As brain over or under (g) In order to perform a hypothesis test for a linear relationship between brain volume (cn3) lincar regression cquation. Round your answer to four decimal places. 3478 cm and a brain weight of 1270g. Report the value of the residual. predicted? Explain within the context of the problem and brain weight(g), we need four assumptions. They are independence of all pairs of observations (xi,yi), (r2, Va) e linear relationship between r and y constant variance of the residuals for all values of r ·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 t Ye/ 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 t 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 as- sumption. (h) what is the 95% confidence interval for ? i. Report the degrees of freedom associated with this confidence interval. ii. What is the correct critical value (from Table D)? ii. Report the lower and upper bounds of your confidence interval. (i) [Free Response.] Interpret the 95% confidence interval for within the context of the problem.

Explanation / Answer

We are allowed to do 4 subparts question at a time. Post again for more subparts of question.

Part a

For the given scenario, the explanatory variable or independent variable is given as brain volume, while the response variable or dependent variable is given as brain weight.

Part b.i.

Sample intercept = b0 = 325.5734

Part b.ii.

Sample slope = b1 = 0.2634

Part c

The slope for the regression line is given as 0.2634 which indicate that there is 0.2634 increment in the brain weight as per unit increment in brain volume. As per one unit increment in explanatory variable brain volume, the response variable brain weight is increased by 0.2634.

Part d

We are given brain volume = 3478 cm3

Regression equation is given as

Brain weight = 325.5734 + 0.2634*Brain volume

Brain weight = 325.5734 + 0.2634*3478

Brain weight = 1241.6790 gram

Part e

Residual = Actual weight – predicted weight

Actual weight = 1270

Predicted weight = 1240

Residual = 1270 – 1240 = 30

Residual = 30

Part f

Based on the part e, Mr. A’s brain was under predicted, because predicted weight of brain is less than actual weight of brain.

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