Question

A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate (X) to predict the number of defects (Y). The following data were collected for 4 randomly selected hours.

Defects (Y)	Production Rate Per Hour (X)
20	400
30	450
10	350
20	375
30	400
25	400
30	450

Determine:

1. SS_x
2. SS_y
3. SS_xy.
4. What you can say about correlation for these two variables (strong, weak, moderate). Explain your reasoning.
5. Calculate the estimates for the slope β1 and intercept β0.
6. Write the estimate of the least square regression line.

   7.What is defect size if x=500?

8~9. The sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468.

8. What is the test statistic value for testing whether the true population correlation coefficient is equal to zero? (calculate t-test statistic)    

9. What is the t- critical value for alpha= 0.01. and what you can conclude about population correlation ( is there significant correlation between two variables).

Answer 1

Note : The first set of questions related to regression are solved. Allowed to solve only 4 questions per post.

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Determine:
SSx
SSy
SSxy.
Calculate the estimates for the slope β1 and intercept β0
Write the estimate of the least square regression line.

Below given are the answers for the all above question.

Step 1 : find the following statistics.

7.What is defect size if x=500?

What you can say about correlation for these two variables (strong, weak, moderate). Explain your reasoning.

Correlation between the two variable is strong.

Explanation
Correlation between two variables define the strength and the relationship between two varible.
By strength we mean, how strong or weak is the association between the two variables.

The correlation coefficient takes a value between 0 and 1 and it can have a positive or negative sign depending on the relationship.

Higher the value, stronger is the relationship.
A positive sign indicates that as one variables increase or decreases, the other variable also increase or decreases in the same proportion.

A negative sign indicates that as one variables increases the other decreases and vice versa.
.