CORRELATION AND REGRESSION

CORRELATION AND REGRESSION

1.       June and Jun are partners in the Chemistry Lab.  Their assignment is to determine how much copper (CuSO4) will dissolve in water at 10, 20, 30, 40, 50, 60, and 70 C.  These lab results are shown below where y is the weight in grams of copper sulfate which will dissolve in 100g of water at X C.  Sketch a scatter diagram. Find the equation of the least squares line and compute Se.

X             10           20           30           40           50           60           70

Y              17           21           25           28           33           40           49

2.       The number of workers on an assembly line varies due to the level of absenteeism on any given day.  In a random sample of production output from several days of work the following data were obtained where x = number  of workers absent from assembly line and y = number of defects coming off the line.

X             3              5              0              2              1              2              7

Y              16           20           9              12           10           13           25

A) Draw a scatter diagram for the data.

B) Find  and b.  What is the equation of the least squares line?

C) Graph the least squares line on your scatter diagram.

D) Find the standard error of estimate Se.

E) Find a 95% confidence interval for the number of defects when four workers are absent.

3.       In placing a weekly order for hotdogs the concessionaire at a large baseball stadium needs to estimate the size of the crowd that will attend the game.  Advanced ticket sales often give a good indication of expected attendance at games.  Data from six previous weeks of games are shown below, where x = advanced ticket sales (in thousands) and y = number of hotdogs purchased (in thousands) at the game.

X             45           64           37           58           41           29

Y              32           46           25           44           32           18

A) Draw a scatter diagram for the data.

B) Find  and b.  What is the equation of the least squares line?

C) Graph the least squares line on your scatter diagram.

D) Find the standard error of estimate Se.

E) Find a 95% confidence interval for the number of hotdogs to be prepared when advanced ticket sales are 55 thousand.

4. The Central Office of a large manufacturing company manager ten similar plants in different locations.  The following data were obtained where x = percent of operating capacity being used at the plant and y = profits in hundreds of thousands of dollars at the same plant.

X             50           61           77           80           82           85           88           81           95           99

Y              24           26           35           31           35           34           39           40           38           42

A) Draw a scatter diagram for the data.

B) Find  and b.  What is the equation of the least squares line?

C) Graph the least squares line on your scatter diagram.

D) Find the standard error of estimate Se.

E) Find a 95% confidence interval for the range of profits of a plant working at 75 percent capacity.

5.  As director of personnel for a prosperous company you have just hired a new public relations person.  The final salary arrangements are negotiated depending on the number of years of experience the new public relations person brings to the company.  After checking with several other companies in your area you obtain the following data where x = number of years of experience for a person in public relations and y = annual salary in thousands of dollars.

X             1              2              15           11           9              6

Y              25           29           53           49           37           34

A) Draw a scatter diagram for the data.

B) Find  and b.  What is the equation of the least squares line?

C) Graph the least squares line on your scatter diagram.

D) Find the standard error of estimate Se.

E) Estimate a salary range for the candidate so that approximately 95% of the public relations officers with 8 years of experience will be in this range.

final exam

PRESENT THE RESULTS OF THE FOLLOWING PROBLEMS IN A TABULAR FORM AND INTERPRET.

1.        A standardized Mathematics test was given to fourth-grade children in five schools in each of the three Paranaque school districts.  The mean score for each school district follows:

District 1	District 2	District 3
59	58	55
68	63	79
77	72	52
70	55	77
79	80	66

Use the 0.05 level of significance to test the claim that there is no difference in the mean scores from each school district. 

2.       A newspaper publisher trying to pinpoint  his market’s  characteristics, wondered whether newspaper readership in the community is related to reader’s educational achievement.  A survey questioned adults in the area on their level of education and their frequency of readership.  The results are shown in the following table.  Use 0.01 significance level.

Readership	Level of Educational Achievement
	PROFESSIONAL	COLLEGE	HIGH SCHOOL	DID NOT COMPLETE HS
NEVER	7	14	13	16
SOMETIMES	13	17	7	7
MORNING	39	41	8	12
BOTH EDITIONS	22	23	8	12

3.       A class adviser was interested in determining the relationship between the Mathematics grades and Chemistry grades of the top 10 junior students.  She gathered the following data.

Student                                                Mathematics Grade(X)                  Chemistry Grade (Y)

1                                                              84                                                           85

2                                                              89                                                           88

3                                                              84                                                           83

4                                                              86                                                           86

5                                                              84                                                           85

6                                                              84                                                           88

7                                                              87                                                           89

8                                                              94                                                           93

9                                                              88                                                           84

10                                                           85                                                           84

Compute the coefficient of correlation and determine whether there is significant relationship between the two scores at 0.01 level of significance.

4.       A group of 50 college freshmen was randomly assigned to experimental and control groups to determine the effectiveness of a counselling program upon academic averages.  Use any method to test the null hypothesis that there was no difference between the academic performance of the experimental and control groups at the 0.05 level of significance.  Use the data in the following table.

Experimental                                                     Control

                                                                2.10                                                        2.01

                                                                3.00                                                        2.69

                                                                1.96                                                        3.07

                                                                2.04                                                        2.14

                                                                3.27                                                        2.82

                                                                3.60                                                        2.57

                                                                3.80                                                        3.44

                                                                2.75                                                        4.00

                                                                1.98                                                        3.01

                                                                2.00                                                        2.55

                                                                2.98                                                        2.77

                                                                3.10                                                        3.09

                                                                3.69                                                        2.72

                                                                2.66                                                        3.34

                                                                2.56                                                        2.81

                                                                2.50                                                        3.05

                                                                3.77                                                        2.67

                                                                2.40                                                        1.90

                                                                3.20                                                        1.70

                                                                1.71                                                        1.57

                                                                3.04                                                        1.39

                                                                2.06                                                        2.09

                                                                2.86                                                        3.68

                                                                3.02                                                        2.11

                                                                1.88                                                        2.83

5.       A researcher wants to compare the problems met by teachers and head teachers in relation to administration and supervision.  She uses 27 teachers and 18 head teachers as her samples.  The questionnaire and their respective answers are collated and presented.  Test if significant difference exists between the problems met by teachers and head teachers at 0.05 level.

Item Number	Problems	Teacher		Head Teacher
		f	%	f	%
1	Lack of encouragement on the part of teachers to attend in service training, seminars, workshops	18	66.66	8	44.44
2	Lack of support in supplying school materials	26	96.29	13	72.22
3	Lack of opportunity for teachers to grow professionally by enjoying study leave	12	44.44	13	72.22
4	No supervisory help in carrying out community services	25	92.59	10	55.55
5	Lack of will to impose disciplinary measure on erring personnel	15	55.55	17	94.44