Homework answers / question archive / Engineering Probability and Inference Homework 5 In an article “Reactions on Painted Steel Under the Influence of Sodium Chloride, and Combinations Thereof”, measurements were taken of the Sodium Chloride deposition rate and steel weight loss

Engineering Probability and Inference Homework 5 In an article “Reactions on Painted Steel Under the Influence of Sodium Chloride, and Combinations Thereof”, measurements were taken of the Sodium Chloride deposition rate and steel weight loss

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Engineering Probability and Inference Homework 5

1. In an article “Reactions on Painted Steel Under the Influence of Sodium Chloride, and Combinations Thereof”, measurements were taken of the Sodium Chloride deposition rate and steel weight loss.

 

Sodium Chloride, x	14	18	40	43	45	112
Steel Weight Loss, y	280	350	470	500	560	1200

 

1. Find the least-squares regression line relating the steel weight loss to the sodium chloride deposition rate.
2. Do the data provide sufficient evidence to indicate that β₁ is not 0? Use a significance level of 0.05.
3. Find a 95% confidence interval for β₁.
4.  Find a 95% prediction interval for the amount of steel weight loss when the sodium chloride deposition rate is 50.
5.  Find the correlation coefficient for this data.
6. Do the data provide sufficient evidence to show there is a correlation between sodium chloride deposition and steel weight loss? Use a significance level of 0.05.
7. Find the proportion of the variability in steel weight loss that is explained by the linear relationship with sodium chloride deposition rate (ie the coefficient of determination).

 

 

 

 

2.  A political scientist wished to examine the relationship between voter image of a candidate and distance (in miles) between the residences of the voter and the candidate.

 

Rating	12	7	5	19	17	12	9	18	3	8	15	4
Distance	75	200	300	15	180	240	120	60	230	165	130	130

 

Calculate Spearman’s rank correlation coefficient.

 

 

 

 

3. Suppose we want to predict job performance of Chevy mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. Use the data below:

 

Apt Test (X1)	40	45	38	50	48	55	53	55	58	40
Pers Test (X2)	25	20	30	30	28	30	34	36	32	34
Job Performance (Y)	1	2	1	3	2	3	3	4	4	3

 

Apt Test (X1)	55	48	45	55	60	60	60	65	50	58
Pers Test (X2)	38	28	30	36	34	38	42	38	34	38
Job Performance (Y)	5	3	3	2	4	5	5	5	4	3

 

 

 

1. Set up the three normal equations needed to find the multiple regression model. Solve for the betas and give the multiple regression equation.
2. Using the data given below, complete the ANOVA table for this data.

 

Source	df	SS	MS	F
Regression		19.96
Residual
Total	19	29.75

 

 

3. What is the coefficient of determination for this data and what does it mean?