Kindly assist with the solution to this Statistics Homework. The preferred software to be used is JMP
Analysis with Software - Answers can be typed or answered by hand with all work shown for credit. Include only the requested output with the problem for which it is used. Download "Physical.jmp" data in eCampus. The data set consists of measurements for the following five variables: - Height: height (in) - LeftArm: left forearm length (cm) - Nose: nose length (cm) - HeadCirc: head circumference (cm) - LeftFoot: left foot length (cm) We are interested in predicting Height. First, run a multiple linear regression model with LeftArm, Nose, HeadCirc, and LeftFoot, and answer the following questions. We assume that the significance level is 0.05 throughout the questions. 1. (1 pt) State the theoretical multiple linear regression model in the context of the problem. 2. (1 pt) Report the equation for the estimated regression model in the context of the problem. (Put relevant JMP outputs in this blank). 3. (1 pt) Report the estimated slope for LeftArm and interpret it in the context (specify the units). 4. (2pts) Calculate Adjusted R2 and state why we should consider using Adjusted R2 inst ead of R2 in the setting of multiple linear regression. 5. Conduct a hypothesis test to see if at least one from LeftArm, Nose, HeadCirc, and LeftF oot is useful in predicting Height? i. (1 pt) State the null and alternative hypotheses. ii. (1 pt) State the full the reduced models. iii. Answer the following questions. a. (1 pt) Should we reject the null or fail to reject the null? b. (2 pts) Justify your decision in a. using a rejection region. c. (1 pt) Justify your decision in a. using a p-value. (Put relevant JMP outputs in this question) iv. (1 pt) Interpret your conclusion in the context. 6. Conduct a hypothesis test to determine whether Nose is a useful predictor of Height, given that all other variables remain in the model. i. (1 pt) State the null and alternative hypotheses. ii. (1 pt) State the full the reduced models. iii. Answer the following questions. a. (1 pt) Should we reject the null or fail to reject the null? b. (2 pts) Justify your decision in a. using a rejection region. c. (1 pt) Justify your decision in a. using a p-value. (Put relevant JMP outputs in this blank) iv. (1 pt) Interpret your conclusion in the context. As shown in your JMP outputs from question 5, the coefficients for Nose and HeadCirc might not be helpful to predict Height. 7. Conduct a hypothesis test to determine whether Nose and HeadCirc can be dropped fro m the model. i. (1 pt) State the null and alternative hypotheses. ii. (1 pt) State the full the reduced models. iii. Answer the following questions. a. (1 pt) Should we reject the null or fail to reject the null? b. ( 2 pts) Justify your decision in a. using a rejection region. c. (1 pt) Justify your decision in a. using a p-value. (Put relevant JMP outputs in this blank) iv. (1 pt) Interpret your conclusion in the context. Analysis with Software - Answers can be typed or answered by hand with all work shown for credit. Include only the requested output with the problem for which it is used. Download "Physical.jmp" data in eCampus. The data set consists of measurements for the following five variables: - Height: height (in) - LeftArm: left forearm length (cm) - Nose: nose length (cm) - HeadCirc: head circumference (cm) - LeftFoot: left foot length (cm) We are interested in predicting Height. First, run a multiple linear regression model with LeftArm, Nose, HeadCirc, and LeftFoot, and answer the following questions. We assume that the significance level is 0.05 throughout the questions. 1. (1 pt) State the theoretical multiple linear regression model in the context of the problem. 2. (1 pt) Report the equation for the estimated regression model in the context of the problem. (Put relevant JMP outputs in this blank). 3. (1 pt) Report the estimated slope for LeftArm and interpret it in the context (specify the units). 4. (2pts) Calculate Adjusted R2 and state why we should consider using Adjusted R2 inst ead of R2 in the setting of multiple linear regression. 5. Conduct a hypothesis test to see if at least one from LeftArm, Nose, HeadCirc, and LeftF oot is useful in predicting Height? i. (1 pt) State the null and alternative hypotheses. ii. (1 pt) State the full the reduced models. iii. Answer the following questions. a. (1 pt) Should we reject the null or fail to reject the null? b. (2 pts) Justify your decision in a. using a rejection region. c. (1 pt) Justify your decision in a. using a p-value. (Put relevant JMP outputs in this question) iv. (1 pt) Interpret your conclusion in the context. 6. Conduct a hypothesis test to determine whether Nose is a useful predictor of Height, given that all other variables remain in the model. i. (1 pt) State the null and alternative hypotheses. ii. (1 pt) State the full the reduced models. iii. Answer the following questions. a. (1 pt) Should we reject the null or fail to reject the null? b. (2 pts) Justify your decision in a. using a rejection region. c. (1 pt) Justify your decision in a. using a p-value. (Put relevant JMP outputs in this blank) iv. (1 pt) Interpret your conclusion in the context. As shown in your JMP outputs from question 5, the coefficients for Nose and HeadCirc might not be helpful to predict Height. 7. Conduct a hypothesis test to determine whether Nose and HeadCirc can be dropped fro m the model. i. (1 pt) State the null and alternative hypotheses. ii. (1 pt) State the full the reduced models. iii. Answer the following questions. a. (1 pt) Should we reject the null or fail to reject the null? b. ( 2 pts) Justify your decision in a. using a rejection region. c. (1 pt) Justify your decision in a. using a p-value. (Put relevant JMP outputs in this blank) iv. (1 pt) Interpret your conclusion in the context
