Problem

The following data show Morningstar's Fair Value …

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Problem 50 Easy Difficulty

The data in the following table show the number of shares selling (millions) and the
expected price (average of projected low price and projected high price) for 10 selected
initial public stock offerings.
a. Develop an estimated regression equation with the number of shares selling as the
independent variable and the expected price as the dependent variable.
b. At the .05 level of significance, is there a significant relationship between the two
variables?
c. $\quad$ Did the estimated regression equation provide a good fit? Explain.
d. Use the estimated regression equation to predict the expected price for a firm considering an initial public offering of 6 million shares.

Answer

See explanation

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Intro Stats / AP Statistics

Essentials of Modern Business Statistics

Chapter 12

Simple Linear Regression

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Video Transcript

here's data looking at stock prices and their stock shares and the expected price and the shares are in millions and I guess the prices and dollars. So developing an estimated regression equation with the number of shares selling as the independent variable and the expected prices that deep in it. So here is your is your data and we want to make a a regression equation. So go ahead and you don't even need to highlight. Go to data and then data analysis and then regression and somebody's going from B. Two to B. 11 for the Y. Input. And then um the X. Is a 2 to 11 if you want you can look at the residuals that might help. Um And heck even line fit plots is fine. So then if we go here and that basically gives us everything we need. So the regression equation voting, write this down. So the regression equation we look at the intercepts here. So the intercept are the coefficients I shouldn't say intercept. So why Pat is nine Let's say 2 6 And then plus seven we'll say one X. All right. So that's part a. Is the regression line. Okay so that's part that part's done now at the point of five level of significance. Is there a significant relationship between the two variables? And uh let's look at this f statistic that p value Equals .001 which is less than alpha and whenever it's less than alpha then you're always going to reject. H not and h not in this case is that there is not a significant relationship. So H. A. Is that there is a significant relationships. That means there is a significant relationship. Okay okay. And then part C. It says use the estimated regression or did the estimated regression equation provide a good fit? And I would say yes. So the r squared is 74% which means we can explain 74% of the ah variation in price by the number of shares. That's a pretty high number. And then you can also look at the are that correlation coefficients quite high? You can also look at the residual plot. So the residual plot here we have apparent randomness to our residuals which means the linear model um is the best model. So I would say yes there you can see those residuals are pretty small as well and you know just kind of beating a dead horse here. But you can also look at the scatter plot. Um If you go to insert okay and that looks pretty tight and you can add some stuff to this. So you can add like a trend line. For example, that's the same thing as a regression line. And you see it's pretty close it it kind of hits right around all those points. So I would say yes. And then the last part of that question, it says using the estimated regression predict the expected price for firm That has six million shares. So your x. value there is six. So we're just making a quick prediction here. So why had equals 9.26 Plus .71 times six and Just take out the calculator. I actually haven't done it yet. So 9-6 Plus .71 times six. And that gives you about 13.52. The estimated price Of that share will be 1352. And I don't know the scale here, I can't remember but but that's uh that seems like a reasonable prediction there.

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