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Simple regression and hypothesis testing for correlation

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1.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, 3 employees were assigned to assemble the subassemblies. They produced 8 during a one-hour period. Then 5 employees assembled them. They produced 13 during a one-hour period. The complete set of paired observations follows.

Number of
Assemblers One-Hour
Production (units)
3 8
5 13
2 5
6 23
4 16

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.

PictureClick here for the Excel Data File (I will upload this)

b. A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production?

Picture
, as the number of assemblers , so does the production.

c. Compute the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round sx, sy and r to 3 decimal places.)

X Y Picture Picture (Picture )2 (Picture )2 (Picture )(Picture )
3 8
-5
25

5 13 1
1
0
2 5
-8
64

6 23 2
4
20
4 16
3 0
0

Picture =
Picture =
sx =

sy =
r =
2. The following sample observations were randomly selected. (Round your answers to 2 decimal places.)

X:
4
5
3
6
10
Y:
9.8
9.6
8
14.4
19.6

a. The regression equation is formula17.mml =
+
X

b. When X is 9 this gives formula17.mml =

3. Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New England. The general sales manager aired a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She obtained the information for Saturday-Sunday digital camera sales at the various outlets and paired it with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are:

Location of Number of Saturday-Sunday Sales
TV Station Airings ($ thousands)
Providence 4 15
Springfield 2 8
New Haven 5 21
Boston 6 24
Hartford 3 17

PictureClick here for the Excel Data File (I will upload this)

a. What is the dependent variable?

is the dependent variable.

c. Determine the correlation coefficient. (Round your answer to 2 decimal places.)

Coefficient of correlation

d. Interpret these statistical measures.

The statistical measures obtained here indicate correlation between the variables.

4. The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)
1 9 8.1 7 8 7.6
2 7 6.0 8 11 8.0
3 11 3.6 9 10 8.0
4 12 4.0 10 12 6.0
5 8 5.0 11 6 8.6
6 7 10.0 12 6 8.0

Picture Click here for the Excel Data File

a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable?

is the independent variable and is the dependent variable.

b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

X Y Picture Picture (Picture )2 (Picture )2 (Picture )(Picture )
9.0 8.1
1.192 0.007 1.420 0.099
7.0 6.0
-0.908 3.674 0.825 1.741
11.0 3.6 2.083
4.340 10.945 -6.892
12.0 4.0 3.083
9.507 8.458 -8.967
8.0 5.0 -0.917 -1.908
3.642 1.749
7.0 10.0 -1.917 3.092
9.558 -5.926
8.0 7.6 -0.917 0.692 0.840
-0.634
11.0 8.0 2.083 1.092 4.340
2.274
10.0 8.0 1.083 1.092 1.174 1.192

12.0 6.0 3.083 -0.908 9.507 0.825

6.0 8.6 -2.917 1.692 8.507 2.862 -4.934
6.0 8.0 -2.917 1.092 8.507 1.192 -3.184
107.000 82.900

Picture =
Picture =
sx =
sy =

r =

b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.)

correlation between age of car and selling price. So,
% of the variation in the selling price is explained by the variation in the age of the car.

5. Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78.

At the .01 significance level, is the correlation in the population greater than zero? (Round your answer to 3 decimal places.)

The test statistic is
.

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The solution gives detailed steps on solving a series of questions on simple regression and hypothesis testing for correlation.

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1 b. A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production?
Yes, as the number of assemblers increase, so does the production.

1 c.
X Y X-
Y-
(X- )2
(Y- )2
(X- )(Y- )

3 8 -1 -5 1 25 5
5 13 1 0 1 0 0
2 5 -2 -8 4 64 16
6 23 2 10 4 100 20
4 16 0 3 0 9 0
20 65 10 198 41
=20/5=4 =65/5=13
Sx=sqrt[10/(5-1)]=1.581
Sy=sqrt[198/(5-1)]=7.036
Sxy=41/(5-1)=10.250
r=10.25/[1.581*6.874]=0.921

2 a. ...

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