Answer to Question #183398 in Statistics and Probability for Lamees

Question

Assuming the following table of the cost (X) and selling (Y) price of flight tickets in dollars ($):

Cost Price

(X)

Sell Price

(Y)

200 300

230 250

500 510

540 700

670 730

320 500

190 412

280 355

625 635

Compute the following:

1. Plot a scatter plot of the data (manual plot or use any software like excel). (2 marks)

2. Pearson correlation coefficient (r). (2 marks)

3. The relation type and strength. (1mark)

4. Linear regression formula (𝑌̂

𝑖 = 𝛽̂

0 + 𝛽̂

1𝑋𝑖

). (2 marks)

5. The estimated of the ticket selling price when the cost is $500. (1 mark)

6. The error of the ticket selling price estimate when the cost is $500. (1 mark)

7. What is the percent of cost price variable interpret the variation of sell price variable

(How much the coefficient of determination)? (1 m

Answer 1

$\bar{X}=\dfrac{\sum X}{n}=\dfrac{3555}{9}=395, \bar{Y}=\dfrac{\sum Y}{n}=\dfrac{4392}{9}=488$

1.The plot of the data is-

2.Pearson's correlation coefficient-

$r=\dfrac{\sum(x-\bar{x})(y-\bar{y})}{\sqrt{\sum(x-\bar{x})^2\sum(y-\bar{y})^2}}$

$=\dfrac{223995}{\sqrt{286700\times 237457}}=\dfrac{223995}{260895.06}=0.858$

3.There is a positive relation and the strength between Cost price and selling price is good.

4.Regression equation of y on x-

$y-\bar{y}=r(x-\bar{x})\\y-488=0.858(x-395)\\\Rightarrow y=0.858x+148.9$

5.Estimeted of the ticket selling when cost is $500-

$y=0.858\times 500+148.9=577.9$

6.Error of the ticket selling price estimate when the cost is $500

$=577.9-510=67.9$

7. coefficient of determination-

$=\dfrac{n\sum(XY)-\sum X \sum Y}{\sqrt{[n\sum X^2-(\sum X)^2][n\sum Y^2-(\sum Y)^2}}$

$=\dfrac{9(1633955)-(3555)(4392)}{\sqrt{[9(1690925)-(3555)^2][9(2384494-(4392)^2]}}$

$=\dfrac{-907966}{\sqrt{2580300\times 2170782}}=\dfrac{-907966}{2366699.88}=-0.383$