Q. 4.153 - Elementary Statistics

Question

In each of Exercises 4.152 and 4.153. perform the following tasks.

 a. Compute the linear correlation coefficient, r.

b. Can you conclude from your answer in part (a) that the variables x and y are linearly related? Explain your answer price data for

c. Draw a scatterplot for the data.

d. Is use of the linear correlation coefficient as a descriptive measure for the data appropriate? Explain your answer.

e. Show that the data are related by the equation provided.

f. Graph the equation and the date points.

x	0	1	2	3	4	5	6
y	0	1	4	9	16	25	36

Step-by-Step Solution

Answer

The output of the graph is 

Step 1. Given

x	0	1	2	3	4	5	6
y	0	1	4	9	16	25	36

Step 2. MINITAB Procedure

Step 1: Select Statistics> Basic Statistics> Connectivity.

Step 2: In the variable, select x and y in the box on the left.

Step 3: Click OK.

Step 3. MINITAB output

Correlations : x, y

The correlation coefficient , r is 0.961.

Step 4. Explanation

 Based on the result obtained in subsection (a), it cannot be concluded that the variables x and y are correlated. Picture information is also required whether the points are scattered on the line or not.

Step 5. Construct a scatterplot

Minitab procedure

MINITAB process:

Step 1: Select Graph> Scatterplot

Step 2: Select By Connection Line, then click OK.

Step 3: Under the Y variable, enter the y column

Step 4: Below the X variable, enter the x column.

Step 5: Click OK.

Step 6. Minitab output

Step 7. Solution d

Check whether the use of the linear coefficient as a descriptive measure of data is appropriate or not.

No, using a line coefficient of line as a descriptive measure of data is incorrect because from the scatterplot, it is clear that the given data pattern is not linear.

Step 8. Show that the related equation provided

For x=0.

Substitute 0 for x in the regression equation. Therefore.

y-x²

= (0)²

<=0

$$\begin{gathered} \mathrm{For} \mathrm{x} = 1. \\ \mathrm{Substitute} 1 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation}. \\ \mathrm{Therefore}, \mathrm{y}=\mathrm{x}² =\left(1\right) \\ \mathrm{For} \mathrm{x}=2. \\ \mathrm{Substitute} 2 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation}. \\ \mathrm{Therefore}, ={\left(2\right)}^2=4 \\ \mathrm{For} \mathrm{x}=3. \\ \mathrm{Substitute} 3 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation}. \mathrm{Therefore}, \\ \mathrm{Substitute} 3 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation}. \\ \mathrm{Therefore}, =\left(3\right)² =9 \\ \mathrm{For} \mathrm{x}=4. \\ \mathrm{Substitute} 4 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation}. \\ \mathrm{Therefore}, =\left(4\right)² =16 \\ \mathrm{For} \mathrm{x}=5. \\ \mathrm{Substitute} 5 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation}. \\ \mathrm{Therefore}, =\left(5\right)² = 25 \\ \mathrm{For} \mathrm{x}=6. \\ \mathrm{Substitute} 6 \mathrm{for} \mathrm{x} \mathrm{in} \mathrm{the} \mathrm{regression} \mathrm{equation} \\ \mathrm{Therefore}, =\left(6\right)2 = 36 \end{gathered}$$

Step 9. Graph the equation

Minitab Procedure

Step 1: Select Graph> Scatterplot

Step 2: Select By Connection Line, then click OK

Step 3: Under Y variables, enter the y y column

Step 4: Below the X variable, enter the x column.

Step 5: Click OK.

Minitab output