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Correlation , regression analysis and ANOVA

FOR YOUR EMAIL YOU USE A FILTER TO BLOCK SPAM FROM YOUR INBOX. THE NUMBER OF ITEMS BLOCKED BY DAY OF WEEK IS RECORDED AND A STATISTICAL SOFTWARE SYSTEM IS USED TO PERFORM THE ANALYSIS THAT FOLLOWS. HERE ARE THE RESULTS.

SOURCE DF SS MS F P
FACTOR 6 1367.8 228 5.72 0
ERROR 48 1913.2 39.9
TOTAL 54 3281
S=6.313 R-SQ=41.69% R-SQ(ADJ)=34.40%

individual 95% cis for mean based on pooled st dev
Level N MEAN ST DEV---------+--------+-----+-----------+-------------
MONDAY 10 74 6.164 (-------*-----------)
TUESDAY 9 66.111 7.288 (-----+------)
WED 7 74.143 2.268 (-----------*-------------)
THURS 8 62.375 5.041 (-------*-------)
FRIDAY 8 75.125 4.454 (-----------*----------)
SAT 5 63.2 7.259 (-------*--------------)
SUN 8 72.375 9.164 (---------*----------)

60 66 72 78

USE THE .05 LEVEL OF SIGNIFICANCE LEVEL TO TEST IF THIS EVIDENCE SUGGESTS A DIFFERENCE IN THE MEANS FOR THE DIFFERENT DAYS OF THE WEEK.

56. THE FOLLOWING TABLE SHOWS THE MEAN ANNUAL PERCENT RETURN ON CAPITAL AND THE MEAN ANNUAL PERCENTAGE SALES GROWTH FOR EIGHT AEROSPACE AND DEFENSE COMPANIES.

COMPANY PROFITABILITY GROWTH
ALLIANT TECH 23.1 8
BOEING 13.2 15.6
GENERAL D 24.2 31.2
HONEYWELL 11.1 2.5
L-3 10.1 35.4
NORTHROP 10.8 6
ROCKWELL 27.3 8.7
UNITED 20.1 3.2

A. COMPUTE THE COEFFICIENT OF CORRELATION. CONDUCT A TEST OF HYPOTHESIS TO DETERMINE IF IT IS REASONABLE TO CONCLUDE THAT THE POPULATION CORRELATION IS GREATER THAN ZERO. USE A .05 LEVEL OF SIGNIFICANCE.
B. DEVELOP A REGRESSION EQUATION OF PROFITABILITY BASED ON GROWTH. COMMENT ON THE SLOPE VALUE.
C. USE A SOFTWARE PACKAGE TO DETERMINE THE RESIDUAL FOR EACH OBSERVATION. WHICH COMPANY HAS THE LARGEST RESIDUAL?

59. A DOG TRAINER IS EXPLORING THE RELATIONSHIP BETWEEN THE SIZE OF THE DOG (WEIGHT IN LBS) AND ITS DAILY FOOD CONSUMPTION (MEASURED IN STANDARD CUPS). BELOW IS THE RESULT OF A SAMPLE OF 18 OBSERVATIONS.

DOG WEIGHT CONSUMPTION
1 41 3
2 148 8
3 79 5
4 41 4
5 85 5
6 111 6
7 37 3
8 111 6
9 41 3
10 91 5
11 109 6
12 207 10
13 49 3
14 113 6
15 84 5
16 95 5
17 57 4
18 168 9

A. COMPUTE THE CORRELATION COEEFICIENT. IS IT REASONABLE TO CONCLUDE THAT THE CORRELATION IN THE POPULATION IS GREATER THAN ZERO? USE A .05 LEVEL OF SIGNIFICANCE.
B. HOW MUCH DOES EACH ADDITIONAL TEN POUNDS OF WEIGHT CHANGE THE ESTIMATED NUMBER OF CUPS OF DOG FOOD CONSUMED?
C. IS ONE OF THE DOGS A BIG UNDEREATER OR OVEREATER?

Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

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