Answer to Question #174993 in Statistics and Probability for Ceejay

Question

A. Construct a scatterplot of the following bivariate data:

1. 

Age of person, in years  | 11 | 12 | 13 | 14 | 15 |

Weight (kg)            | 40 | 42 | 38 | 45 | 51 |   

2. 

Age of car, in years   | 11 | 12 | 13 | 14 | 15 | 

Mileage, in km/liter   | 40 | 42 | 38 | 45 | 51 | 

B. Identify the dependent and independent variable in each of the following pairs of variables. Write your answer on the space provided

1. The base and the area of the triangle.

Independent Variable:

Dependent Variable:

2. Cost and age of car.

Independent Variable:

Dependent Variable:

3. The age and birth date.

Independent Variable:

Dependent Variable

Answer 1

A.

1.

$$\bar{X}=\dfrac{1}{n}\sum_iX_i=\dfrac{65}{5}=13$$

$$\bar{Y}=\dfrac{1}{n}\sum_iY_i=\dfrac{216}{5}=43.2$$

$$SS_{XX}=\sum_iX_i^2-\dfrac{1}{n}(\sum_iX_i)^2$$

$$=855-\dfrac{(65)^2}{5}=10$$

$$SS_{YY}=\sum_iY_i^2-\dfrac{1}{n}(\sum_iY_i)^2$$

$$=9434-\dfrac{(216)^2}{5}=102.8$$

$$SS_{XY}=\sum_iX_iY_i-\dfrac{1}{n}(\sum_iX_i)(\sum_iY_i)$$

$$=2833-\dfrac{65(216)}{5}=25$$

$$r=\dfrac{SS_{XY}}{\sqrt{SS_{XX}}\sqrt{SS_{YY}}}$$

$$r=0.7797$$

$$r^2=0.6080$$

$0.4<r<0.7$ Moderate positive correlation.

$$Y=n+mX$$

$$m=\dfrac{SS_{XY}}{SS_{XX}}=2.5$$

$$n=\bar{Y}-m\bar{X}=10.7$$

$$Y=10.7+2.5X$$

2.

$$\bar{X}=\dfrac{1}{n}\sum_iX_i=\dfrac{65}{5}=13$$

$$\bar{Y}=\dfrac{1}{n}\sum_iY_i=\dfrac{216}{5}=43.2$$

$$SS_{XX}=\sum_iX_i^2-\dfrac{1}{n}(\sum_iX_i)^2$$

$$=855-\dfrac{(65)^2}{5}=10$$

$$SS_{YY}=\sum_iY_i^2-\dfrac{1}{n}(\sum_iY_i)^2$$

$$=9434-\dfrac{(216)^2}{5}=102.8$$

$$SS_{XY}=\sum_iX_iY_i-\dfrac{1}{n}(\sum_iX_i)(\sum_iY_i)$$

$$=2833-\dfrac{65(216)}{5}=25$$

$$r=\dfrac{SS_{XY}}{\sqrt{SS_{XX}}\sqrt{SS_{YY}}}$$

$$r=0.7797$$

$$r^2=0.6080$$

$0.4<r<0.7$ ​Moderate positive correlation

$$Y=n+mX$$

$$m=\dfrac{SS_{XY}}{SS_{XX}}=2.5$$

$$n=\bar{Y}-m\bar{X}=10.7$$

$$Y=10.7+2.5X$$

B.

1. The base and the area of the triangle.

Independent Variable: base

Dependent Variable: area

2. Cost and age of car.

Independent Variable: age of car

Dependent Variable: cost

3. The age and birth date.

Independent Variable: birth date

Dependent Variable: age