MATH SOLVE

5 months ago

Q:
# Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction.Price in dollars 23 29 32 38 41Number of Birds 10 14 15 16 17A) Step 1 of 3: Draw a scatter plot of the given data.B)Step 2 of 3: Estimate the correlation in words: positive, negative, no correlation.C) Step 3 of 3: Calculate the correlation coefficient, r. Round your answer to three decimal places

Accepted Solution

A:

Answer:Step 1: Figure attachedStep 2: Positive correlationStep 3: r=0.9534Step-by-step explanation:Step 1For this step we can use excelWe click on Insert> Insert Scatterpplot(X,Y) or Bubblechart. We select the data and then we select the Layout 9. Then we can edit the title and the names for the x and y axis.The result obtained is on the Figure attached.Step 2As we can see on the plot obtained the slope obtained is positive since is increasing, so with this result we can conclude that the correlation would be positive and possible strong. We need to compute it in order to be sure of this.Step 3In order to calculate the correlation coefficient we can begin doing the following table:n x y xy x*x y*y1 23 10 230 529 1002 29 14 406 841 1963 32 15 480 1024 2254 38 16 608 1444 2565 41 17 697 1681 289[tex] n =5 \sum x \sum y \sum xy \sum x^2 \sum y^2[/tex]n=5 [tex] \sum x = 163, \sum y = 72, \sum xy 2421, \sum x^2 =5519, \sum y^2 =1066[/tex] And in order to calculate the correlation coefficient we can use this formula:[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex][tex]r=\frac{5(2421)-(163)(72)}{\sqrt{[5(5519) -(163)^2][5(1066) -(72)^2]}}=0.9534[/tex]So then the correlation coefficient would be r =0.9534