The table below shows the quarterly earnings per share of a corporation over the
ID: 3296361 • Letter: T
Question
The table below shows the quarterly earnings per share of a corporation over the most recent 7 years.
QTR1 QTR2 QTR3 QTR4
Year 1 .786 .668 .863 .807
Year 2 .802 .670 .885 .805
Year 3 .579 .423 .904 .851
Year 4 .430 .409 1.120 .958
Year 5 .680 .460 1.190 .830
Year 6 .766 .440 1.020 .630
Year 7 .690 .600 1.130 .680
Enter the data into one column of an Excel spreadsheet in chronological order. .786 is the first observation (Year 1 QTR1), .668 the second (Year 1 QTR2), .863 the third, and .680 the twenty-eighth (Year 7 QTR4).
In the next column, create a time variable (it keeps track of how many quarters have passed since a starting point). .786 is matched with 1, .668 is matched with 2, and .680 is matched with 28.
a. Create the appropriate plot of this time series data set. b. Use Data Analysis in Excel (and the regression option) to run a simple linear trend model. c. Based upon the output, please do the following: 1) write out the estimated equation. 2) predict the next value in the time series. 3) interpret the slope coefficient for time. 4) test whether or not there is an upward trend in the value of new housing units. Use alpha = 0.05. 5) identify the value of the p-value for the model test. 6) interpret the coefficient of determination for the model. 7) test whether or not the model has explanatory power. 8) construct and interpret a 98% confidence interval for the population slope coefficient. 9) what is the residual for the second quarter of year 3. d. Now expand your model from a simple linear trend to a trend model that includes seasonal dummy variables (designed to isolate differences across quarters). Use quarter 4 as your reference (or base) quarter. Your spreadsheet should have five columns of data, the earnings per share column, the time variable column, and three columns for the quarters excluding the base quarter. The quarter columns should just be zeros and ones depending upon what quarter is associated with that value of earnings per share.
Explanation / Answer
a]
b]
c_1] Estimated equation is Y = 0.7381 + 0.001X where Y be the earning variable and X be the time variable.
c_2] Prediction of next value that is X = 29 we get Y = 0.7381 + 0.001*29 = 0.767
c_3] Slope interprtation: If earning increase by 1 unit, we predict the earning of corporation will approximately increase by 0.001 unit.
c_5] P-value of the model calculated in part b] is 0.8471
c_6] interpretation of the coefficient of determination for the model = R^2 = 0.001456 is a measure of how much of the variability in one variable can be "explained by" variation in the other. That is 0.15% of the variation in Earning is determined by the linear relationship between Earning and time.
c_8]
98% confidence interval for the population slope coefficient is given in above summary table (-0.01180, 0.01382)
Interpretation: in this interval 0 is included hence there is no statistically meaningful or statistically significant between the Y and X.
c_9]
second quarter of year 3 means as serially residual corresponding to 10 is -0.325 (difference between actual value and predicted value).
SUMMARY OUTPUT Regression Statistics Multiple R 0.038160144 R Square 0.001456197 0.145619658 Adjusted R Square -0.036949334 Standard Error 0.220952713 Observations 28 ANOVA df SS MS F Significance F Regression 1 0.001851079 0.001851079 0.037916325 0.847124822 Residual 26 1.269322635 0.048820101 Total 27 1.271173714 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 98.0% Upper 98.0% Intercept 0.738119048 0.085800707 8.602715218 4.41197E-09 0.561753169 0.914484927 0.525450856 0.950787239 time 0.001006568 0.00516928 0.194721146 0.847124822 -0.009619039 0.011632176 -0.011806164 0.0138193Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.