Listed below is data on profit and market capitalization for a sample of 15 different firms in U.S. Profit is the y variable and market capitalization is the x variable
Profits Market Capitalization ($ millions) x
($millions) y
296.2 1,936.9
–25 1,171.8
4,085 55,135.8
6,558 97,417.2
12,525 95,198.9
3,394 53,579.7
442.8 12,466.3
633.1 8,894.3
3,528 65,872.4
2,698 25,661.3
1,200.65 19,854.7
11.987 195,643.8
641.8 10,447.8
5,043 66,695.5
5,206 53,558.4
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between market capitalization and profit?
b. Use the data to develop an estimated regression equation that could be used to estimate a firm’s profit based on its market capitalization. What is the estimated regression model?
c. What is the predicted profit for the market capitalization of 70,721.3 (million)?

Looking at the graphic it seems that there is a positive regression between the profit and the market capitalization, meaning that every time the market capitalization of the firm increases, the profit of this firm also increases. But not all the "firms" adjust linearly, so I wouldn't expect the regression to be powerful.

b.

The regression model is E(Yi)= α + βXi

Where the parameters of the model are α and β, these two parameters are to be estimated to estimate the regression equation. The estimator for α is a and the estimator for β is b:

a= Y[bar] - bX[bar]

b= [∑XY-(∑X*∑Y)/n]/[∑X²-(∑X)²/n]

I'll use a statistic software to calculate the estimated regression equation:

^Yi= a + bXi

^Yi= 325.89 + 0.07Xi

c.

You need to predict the value of Y (Profit) given a value of X= 70721.3 (million). To make this prediction you have to use the estimated equation:

^Yi= 325.89 + 0.07Xi

^Yi= 325.89 + 0.07(70721.3)= 5276.381

The predicted profit for a market capitalization value of 70,721.3 is 5276.381 million.

I hope this helps!