Morningstar analyzes balance sheets of publicly traded companies and, using a pr
ID: 3182331 • Letter: M
Question
Morningstar analyzes balance sheets of publicly traded companies and, using a proprietary formula, computes a “Fair Value” for the stock price of the company. For a number of randomly selected companies, a researcher records the Morningstar Fair Value and the latest closing price of the stock. Based on this data, she builds a regression model as a first step to determining if the Fair Value is a good predictor of the stock price. She then uses the model to make stock price predictions. The results are shown below. Use them to answer the questions that follow.
Descriptive Statistics: Fair Value ($), Share Price ($)
Total
Variable Count Mean StDev Minimum Maximum
Fair Value ($) 28 54.46 23.62 15.00 98.00
Share Price ($) 28 46.64 24.54 11.02 103.05
Model Summary
S R-sq R-sq(adj) R-sq(pred)
12.0064 76.94% 76.06% 73.25%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -2.99 5.79 -0.52 0.610
Fair Value ($) 0.9113 0.0978 9.31 0.000 1.00
Regression Equation
___________________________________________________________
Fits and Diagnostics for All Observations
Share
Obs Price ($) Fit Resid Std Resid
1 98.63 69.91 28.72 2.49 R
R Large residual
Prediction for Share Price ($)
Regression Equation
____________________________________________
Variable Setting
Fair Value ($) 30
Fit SE Fit 95% CI 95% PI
24.3509 3.29801 (17.5717, 31.1300) (-1.24285, 49.9446)
Variable Setting
Fair Value ($) 90
Fit SE Fit 95% CI 95% PI
79.0275 4.15151 (70.4940, 87.5611) (52.9143, 105.141)
What percentage of variance in the observed Share Price data is explained by the linear relationship with Fair Value?
What is the correlation between Fair Value and Share Price?
In the Coefficients table, Fair Value has a p-value of 0.000. This p-value is in connection with what type of hypothesis test? How many degrees of freedom does this hypothesis test have? Interpret the meaning of this p-value.
Compute a 95% confidence interval for the “population slope” relating the response, Share Price, to the predictor, Fair Value. Under what conditions is this confidence interval valid?
What is the regression equation for this model?
One large residual is noted by Minitab. For this stock (Stock #1), does the regression equation over-estimate or under-estimate the stock price? Briefly explain your answer.
Correctly interpret the 95% confidence intervals and 95% prediction intervals that are computed for this model by Minitab for a stock with Fair Value of 30. Under what conditions are your interpretations of these intervals valid?
Consider more closely the prediction intervals. Note that, for the first of these, the lower endpoint is negative. Can a stock price be negative? What does this suggest about the ability of this model to predict individual stock prices based on Morningstar Fair Value?
Note that, though stock prices change every second of the trading day, Morningstar Fair Value is updated only every 3 months. Thus, it is much more stable. Considering this, how might this model, and in particular the confidence intervals obtained from it, be used in stock investing?
Explanation / Answer
What percentage of variance in the observed Share Price data is explained by the linear relationship with Fair Value?
we need to check r2 value for this. r2 value explains the amount of variation captured by the data. this value ranges from 0 to 100% , higher the better. In this case the value is 76.94%. Hence model is able to explain 77% variation of the data.
What is the correlation between Fair Value and Share Price?
The r2 value is 0.7694 , so the correlation can be calculated as sqrt(r2) = sqrt(0.7694) = 0.8771
In the Coefficients table, Fair Value has a p-value of 0.000. This p-value is in connection with what type of hypothesis test? How many degrees of freedom does this hypothesis test have? Interpret the meaning of this p-value.
The p value is less than 0.05 , hence this means that the variable is significant wrt the fitted model. The hypothesis can be formulated as
H0 : the variable is not significant
H1 : The variable is significant
The degree of freedom is given as n-1 , here the count is 28 , as given in the first table. Hence df = 28-1 = 27
Compute a 95% confidence interval for the “population slope” relating the response, Share Price, to the predictor, Fair Value.
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -2.99 5.79 -0.52 0.610
Fair Value ($) 0.9113 0.0978 9.31 0.000 1.00
using the above table , we can calculate the 95% CI as 0.9113+- z*0.0978, where z = 1.96 for 95% CI from the z table
0.9113+- 1.96*0.0978
(0.71, 1.10)
What is the regression equation for this model?
share price = -2.99 +0.9113*fairvalue
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