Question

The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 13 during a one-hour period. Then 4 employees assembled them. They produced 22 during a one-hour period. The complete set of paired observations follows. Number of Assemblers One-Hour Production (units) 2 14 4 20 1 7 5 23 3 16 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Please answer questions a to d. Please show all steps of derivation. a. Please calculate the sample mean and standard deviation of the number of assemblers and production, respectively. b. Please calculate the correlation coefficient of the number of assemblers and production. c. Please estimate the "a" and "b" in the following equation based on the data above. d. What is the coefficient of determination of the estimated equation in c? What does this value mean intuitively?

          The production department of Celltronics International wants to
explore the relationship between the number of employees who
assemble a subassembly and the number produced. As an experiment, 2
employees were assigned to assemble the subassemblies. They
produced 13 during a one-hour period. Then 4 employees assembled
them. They produced 22 during a one-hour period. The complete set
of paired observations follows.
Number of Assemblers
One-Hour Production (units)
2
14
4
20
1
7
5
23
3
16
The dependent variable is production; that is, it is assumed
that different levels of production result from a different number
of employees. Please answer questions a to d. Please
show all steps of derivation. 
a. Please calculate the sample mean and standard deviation of
the number of assemblers and production, respectively.
b. Please calculate the correlation coefficient of the number of
assemblers and production.
c. Please estimate the "a" and "b" in the following equation
based on the data above.
  
d. What is the coefficient of determination of the estimated
equation in c? What does this value mean intuitively?

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Added by David R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jerelyn Nevil

06/24/2024

Step 1

First, we need to find the sample mean and standard deviation of the number of assemblers and production. Number of Assemblers (X): [2, 4, 1, 5, 3] One-Hour Production (Y): [14, 20, 7, 23, 16] Mean of X: $\bar{X} = \frac{2+4+1+5+3}{5} = \frac{15}{5} = 3$ Mean of Show more…

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The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 13 during a one-hour period. Then 4 employees assembled them. They produced 22 during a one-hour period. The complete set of paired observations follows. Number of Assemblers One-Hour Production (units) 2 14 4 20 1 7 5 23 3 16 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Please answer questions a to d. Please show all steps of derivation. a. Please calculate the sample mean and standard deviation of the number of assemblers and production, respectively. b. Please calculate the correlation coefficient of the number of assemblers and production. c. Please estimate the "a" and "b" in the following equation based on the data above. d. What is the coefficient of determination of the estimated equation in c? What does this value mean intuitively?

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Transcript

00:01 So i see that you need help with this question.

00:02 So this is x and this is y.

00:04 I'm going to calculate your mean of x and then your mean of y.

00:10 So for your mean of x, it's going to be 3.

00:17 And for your mean of y, it's going to be, your mean of y is going to be 16.

00:26 And then you're going to calculate your y minus your mean of y.

00:30 I'm sorry, your x minus your mean of x.

00:36 And then you're going to calculate your y minus your mean of y.

00:40 Then you're going to calculate your x minus your mean of x times your y minus your mean of y.

00:48 And then you're going to calculate your x minus your mean of x x squared, and then your y minus your mean of y squared.

00:59 So the difference between 3 minus 1 is, or 1 minus 3 is a negative 2.

01:08 Then we have 2 minus 3, so it is a negative 1, 0, 1, and 2.

01:18 And then for your y minus your mean of y it's negative 9 because 60 minus 7 negative 9 then negative 2 0 2 0 4 and then 7 and then i'm going to multiply 2 times 9 18 2 0 4 and 14 i'm going to total this up and i'm going to get 38 that's known as my sum of my products then i'm going to square each one of these values so i have 4 1 0 1 and 4 if i total that up i'm going to get 10 then i'm going to calculate the y minus your your mean of y squared.

02:10 And so that is going to be 81, 4, 0, 16, and 49...

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