STATISTICAL ANALYSIS

Statistical Analysis

Statistical Analysis



Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Top Price

93

7.9

80.0

21.899

11.0305

V6

0

MPGTown

93

15

46

22.37

5.620

MPGBest

93

20

50

29.09

5.332

AirBag

93

0

2

.81

.711

HP

93

55

300

143.83

52.374

Length

93

141

219

183.20

14.602

Engine size

93

1.0

5.7

2.668

1.0374

PassCap

93

2

8

5.09

1.039

RPM

93

3800

6500

5280.65

596.732

Weight

93

1695

4105

3072.90

589.897

Valid N (listwise)

0

The above table provide the descriptive statistics for all the variables.

Car price (for basic and top specification models) differs by type of car and how MPG (miles per gallon) differs by type of car.

One Way ANOVA

We say we have a one-way layout when we have a single factor with several levels and multiple observations at each level. With this kind of layout we can calculate the mean of the observations within each level of our factor. The residuals will tell us about the variation within each level. We can also average the means of each level to obtain a grand mean. We can then look at the deviation of the mean of each level from the grand mean to understand something about the level effects. Finally, we can compare the variation within levels to the variation across levels. Hence the name analysis of variance.

Assumptions

The populations from which the samples were obtained must be normally or approximately normally distributed.

The samples must be independent.

The variances of the populations must be equal.

Hypotheses

The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different.

In the following, lower case letters apply to the individual samples and capital letters apply to the entire set collectively. That is, n is one of many sample sizes, but N is the total sample size.

ANOVA

MPGTown

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

1795.204

5

359.041

28.132

.000

Within Groups

1110.366

87

12.763

Total

2905.570

92

From the above table it can be found out that p value is less than level of significance hence here we reject our alternative hypothesis and accept our null hypothesis.

Price and Car Type:

ANOVA

Basic price

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

3075.660

5

615.132

13.508

.000

Within Groups

3961.698

87

45.537

Total

7037.358

92

Again in this case it can be seen that p value is less than level of significance so it lead us to reject alternative hypothesis and accept our null hypothesis.

MPGBest and Car Type:

ANOVA

MPGBest

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

1518.532

5

303.706

24.091

.000

Within Groups

1096.780

87

12.607

Total

2615.312

92

Again in this case it can be seen that p value is less than level of significance so it lead us to reject alternative hypothesis and accept our null hypothesis.

Relationship between MPG and other Variables:

The correlation is one of the most common and most useful statistics. A correlation is a single number that describes the degree of relationship between two variables.

The main result of a correlation is called the correlation coefficient (or "r"). It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related.

If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller (often called an "inverse" correlation).

While correlation coefficients are normally reported as r = (a value between -1 and +1), squaring them makes then easier to understand. The square of the coefficient (or r square) is equal to the percent of the ...