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Profit Forecasting: company interested predicting prafit number of projects based explanatory variables: Measure of risk assigned at the outset of the project (X1 R...

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Profit Forecasting: company interested predicting prafit number of projects based explanatory variables: Measure of risk assigned at the outset of the project (X1 RISK) and the expenditure on research and development for the project (xz RD). Data on the three variables PROFIT, RISK, and RD are available in the worksheet entitled RDS_ PROFIT measured thousands of dollars and RD measured In hundreds of dollars Use the data to fit two separate regression modelsFor the first model (Linear Model AKA

Profit Forecasting: company interested predicting prafit number of projects based explanatory variables: Measure of risk assigned at the outset of the project (X1 RISK) and the expenditure on research and development for the project (xz RD). Data on the three variables PROFIT, RISK, and RD are available in the worksheet entitled RDS_ PROFIT measured thousands of dollars and RD measured In hundreds of dollars Use the data to fit two separate regression models For the first model (Linear Model AKA First Order Model) _ regress PROFIT on the two explanatory variables RISK and RD. (Hint: "Regress PROFIT on x" implies that PROFIT is the variable and is the explanatory variable:) a) State the linear mode equation_ 9 = Ro + B1X1 BzXz Y = Bo + 01*1 + 026,2) Y = Bo 01*1 62*12 Ba*z Y = Bo 064) Bz*z Y = fo 81*1 62*2 Baxz2 However; there some evidence that the relationship between RD and PROFIT is nonlinear: Therefore, next fit the second order polynomial regression model, regress PROFIT RISK, and RDSQR (the squarc of the RD variable) explanatory variables: (Hint: You will have creatc thc RDSQR variablc yoursclf: ) b} State the transformed model equation (i,ev the second order polynomial regression model equation}. Y = Po 81x1 Bz( 9 = Ro R1*1 62X2 9 = Bo + 81*1 Bzxz B3x22 9 = Bo + Bc4)+ Bzx2 9 = Bo B1*1 Bzx12 Baxz



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The management of a company is considering three possible models for predicting the considering three possible models for predicting the company's profits from 2003 through 2008. Model I gives the expected annual profits if the current trends continue. Models II and III give the expected annual profits for various combinations of increased labor and energy costs. In each model, p is the profit (in billions of dollars) and $t=0$ corresponds to 2003. $\begin{array}{ll}{\text { Model I: }} & {p=0.03 t^{2}-0.01 t+3.39} \\ {\text { Model II: }} & {p=0.08 t+3.36} \\ {\text { Model III: }} & {p=-0.07 t^{2}+0.05 t+3.38}\end{array}$ (a) Use a graphing utility to graph all three models in the same viewing window. (b) For which models are profits increasing during the interval from 2003 through $2008 ?$ (c) Which model is the most optimistic? Which is the most pessimistic? Which model would you choose? Explain.

First one. There are 248 families do not want the apples at any price Or two. So distribution is not continuous, There is focal points and rounding for example. Many people report on powder and either 2/3 of a pound or one and a third pounds. This the fact that the distribution of quantity demanded is not continuous violates the underlying assumption of the topic model. Yeah. Which is the Layton error has normal distribution, but we will still explore the Tobin approach in this context. Yeah. It may work better than the linear model for estimating the expected demand function, do you? And Along with Part eight. The estimates from their topic and L. S.. Models are reported in the same table or the tablet model. The price variables ali them are Statistically significant at the one level. The sign over these prize coefficients are in accordance with the demand theory, the own price effect is negative and across price effect is positive. Cross price is the price of this substitute good, which is regular apples part Let's do part 6. 1st part six we will obtain their fitted values and we find that the ranged from 27 8 798 to you. 3.33 at five. The null hypothesis is later one plus beta two equals zero. This is something you can easily test regardless of your statistical package. Yeah. Yeah, you should get a small T statistic about minus point you and a P value of buying eight. So we are unable to reject the North part seven. The squirt correlation between it is E call B. S and it's fitted value is about .04 and that is there are square hard eight. Given the linear model estimates, even this result, we find that the old LS estimate are smaller than the top bit estimate. And in terms of our square oops, you compare the goodness of fit between the two models we look at. There are square mhm. There are squared of the topic. Model is still smaller, slightly smaller than the old LS model and serve. We can conclude that the topic is yeah, no better than the old LS. It doesnt suite the data better. The Last Part, Part nine. The statement is simply incorrect so you could run into a uh counter example. We have valid price effects, but we cannot explain much of the variation in the dependent variable. It's simply difficult to estimate the demand for a fictitious product.

Part one. The results of the progression are Intercept is 1.9 estimate on Eco Price is -2.9 And the estimate on regular price is 3.03. And all of these estimates are highly significant. The r square is very low point 04 and r squared adjusted has similar value. We have 660 observations in our simple, so the simple is not small at all. This model is just not very good. The problem asks you to interpret the result, so this result is as predicted by economic theory. The own price effect is negative and the cross or substitute price effect is positive. An increase in echo price of 10 sense per pound Reduces the estimated demand for Eco label Apples by about .29. Mhm .29 lbs. An increase in regular price of 10 cents per pound for regular apples increases the estimated demand for eco labelled apples by about 0.3 The unit is pound. These effects are quite large in part two. So as I said earlier, each price bearable is individually significant, with a T statistic Greater than four in absolute value. The P values are essentially zero and we conclude that they are significant. Our tree, the fitted values has a minimum of 0.86 and the maximum of 2.09. This is much smaller range than e cole label pounds. The observed demand itself, Which ranged from 0 to 42, Although 42 is kind of an outlier, There are almost 2 50 observations with estimated no not estimated observed demand for eco label apples being zero and these observations are not accounted for in their predicted values. Our sixth, the r square is about 3.6%. This is very small. The model can only explain 3.6, less than 4% of the variation in the demand for eco label apples. The two price variables do not do a good job of explaining why demand varies across families. Part five. We add family income, household size, education and egg to you. Uh The regression that are square increased U exactly 4% and the adjusted osce square falls from point 0342 points 031 We can test the joint significance of the additional variable and the f statistic with four and 653 degrees of freedom has a P value of 0.63 So we are unable to retract the null hypothesis that the estimate on these variables are jointly uh equally zero or six. The problem asked you to run separate simple regressions of demand on price. Of eco labelled opposed and then demand on regular regular price. Yeah. I find that there are square in both cases to be very small, almost zero. And when you calculate the correlation coefficient between eco price and regular price, you would find The coefficient to be .83. So it is possible that the monte culinary t over these variables affect the fit of the model. In part seven we consider a model that adds family income and the quantity demanded for regular apples from basic economic theory. Okay, the regular the man does not belong to the equation. When we estimate the full model, we get our square of point oh six Adjusted r squared of .57 and we will drop the variables one at the time. So if we drop the price of eco labelled variable are square is .03 and at just the square is point 0 to 5. Then if we drop regular price It's just a square is .039. Oh regular, Our square is .039. It's just our square is .035 family income to be dropped. Our square is .06 at just a square is .056. Drop regular apple demand. Our Square is .038. It's just that our square is point oh 34 and all of these are smaller than there are square and adjusted r squared values from their full model. We conclude that the initial old model is still the best.


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