Homework 4

ABC, Inc., sells tea products to various customers. In recent years, profits have been declining. The CFO of the company investigated the reasons for the profit decline and performed regression analysis for sales and costs. She determined that sales depend on product price, delivery speed, customer services, and marketing expenses. She also determined that total costs consist of variable costs of $25 per unit and fixed costs of $56,000. Marketing expenses have a coefficient of determination of 75% related sales.    List two advantages and two limitations of regression analysis.

Question 15 When the R2 of a regression equation is very high, it indicates that all the coefficients are statistically significant. the intercept term has no economic meaning. a high proportion of the variation in the dependent variable can be accounted for by the variation in the independent variables. there is a good chance of serial correlation and so the equation must be discarded.

Write (TRUE/FALSE) for each question.  An observation with a large standardized residual value always generates a large Cook’sdistance value. (T/F)Leverage value detects unusual x values. (T/F)BIC gives heavier penalty on models with many variables than Cp or AIC. (T/F) As the tuning parameter λ → ∞, the coefficients of ridge regression tend to zero. (T/F)Like the least square coefficient, ridge regression coefficients are scale equivalent. (T/F)The shrinkage penalty is applied to all coefficient except for the intercept. (T/F) Lasso regression reduces the bias by increasing the tuning parameter. (T/F)

A multiple regression model, K = a + bX + cY + dZ, is estimated regression software, which produces the following output:   a. Are the estimates of a, b, c, and d statistically significant at the 1 percent significance level? b. How much of the total variation is explained by this regression equation? c. Is the overall regression equation statistically significant at the 1 percent level of significance? d. If X equals 50, Y equals 200, and Z equals 45, what value do you predict K will take?

If the t ratio for the slope of a simple linear regression equation is equal to 1.614 and the critical values of the t distribution at the 1% and 5% levels of significance, respectively, are 3.499 and 2.365, then the slope is   not significantly different from zero.   significantly different from zero at both the 1% and the 5% levels.   significantly different from zero at the 1% level but not at the 5% level.   significantly different from zero at the 5% level but not at the 1% level.   please show how you come up with the answer , do not just guess !!!

Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatterplots and using economic theory, the economist decides to estimate an equation of the form Q=  aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = - 1.3. Now consider two scenarios: (1) the price increases from $10 to $12.50; (2) the price increases from $20 to $25. a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not? b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2? Be as exact as possible.  

In a regression problem with 1 output variable and with a total number of 100 possible input variables, what is the number of all possible models with three input variables?

Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted value of Y in each case? a. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 b. x1 = 23, x2 = 18, x3 = 10, and x4 = 11 c. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 d. x1 = -10, x2 = 13, x3 = -8, and x4 = -16

Quantile regression (QR) is different from OLS in that: a.    QR estimates marginal effects at the mean values of the dependent variables. b.    QR does not estimate marginal effects at the mean values of the dependent and independent variables. c.    QR minimizes the sum of squared residuals to obtain the coefficient estimates. d.     QR only uses the data below the quantile where the quantile regression is being estimated.

The Pilot Pen Company has decided to use 15 test markets to examine the sensitivity of demand for its new product to various prices, as shown in the following table. Advertising effort was identical in each market. Each market had approximately the same level of business activity and population. Complete the following worksheet and then estimate the demand function for Pilot's new pen using a linear regression model. Test Market Price Charged Quantity Sold   (cents) (Thousands of Pens) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 50 20 1,000 2,500 400 2 50 21 1,050 2,500 441 3 55 19 1,045 3,025 361 4 55 19.5 1,072.5 3,025 380.25 5 60 20.5 1,230 3,600 420.25 6 60 19 1,140 3,600 361 7 65 15.5 1,007.5 4,225 240.25 8 65 15 975 4,225 225 9 70 14.5 1,015 4,900 210.25 10 70 15.5 1,085 4,900 240.25 11 80 13 1,040 6,400 169 12 80 14 1,120 6,400 196 13 90 11.5 1,035 8,100 132.25 14 90 11 990 8,100 121 15 40 17 680 1,600 289 Total 980 246     ?…

what are the key features , Strength and limitation of following model? and when which model should be used? Ordinary Least Squares Logit regression model Probit regression model

Questions 1-30 refer to the following scenario: A company reports bi-annual (twice a year) sales data. The sales data for the last three years is shown in below Table. The residual sum of squares of the regression is RSS = a 50 b 70 c 120 d 20   The total sum of squares of the regression is TSS = a 20 b 120 c 70 d 50   The R-squared of the regression is R2= a 0.78 b 0.68 c 0.58 d 0.88   The mean sum of squares of the regression is Mean ESS =  a 20 b 50 c 120 d 70   The mean sum of squares of the residuals is Mean RSS =  a 12.5 b 15.0 c 7.5 d 10.0   You want to test whether the regression in its entirety explains something which is different from zero. For this purpose you use a a Chi-squared test b T-test c E-test d F-test   The value for testing the explanatory significance of the entirety of the regression is a 7.6 b 5.6 c 6.6 d 8.6   The…

XYZ company is interested in quantifying the impact of consumer promotions on the sales of its packaged food product. XYZ has historical data on the following variables for 38 weeks: • Sales: Weekly sales volume in thousands of units.• Prom: Weekly spending on consumer promotions in thousands of Dollars" "A regression analysis was applied to XYZ historical dataset. The dependent variable is weekly Sales and the independent variables are weekly Prom and weekly Lagged Prom (i.e., last week Prom). This is a summary of the regression output:Sales = 0.80 + 1.20*Prom - 0.40*Lag(Prom) • R-squared=0.85• F-Statistic=23.83• p-value=0.001 (for the overall regression)•All regression coefficients are statistically significant at the 5% level." A. What will be the predicted sales volume ? B. What is the gross margin of this net volume impact due to $1000 spending per week on consumer promotions, if brand makes $2.20 gross margin per unit . C. What is the ROI of this promotion? D. What is predicted…

1-R2 k -1 b-briefly explain the reasons for the following statements to be true or false - The classical linear regression model is concerned with heteroskedacity, autocorelation, and multiple linear connection main mass, which express deviations from its assumptions. If the H0 hypothesis is rejected according to the F test and the H0 hypothesis cannot be rejected for all parameters according to the T test, the problem here is which variables will be excluded from the model. - R2 value is high due to trend effect while working with cross-sectional data in Applied Studies× R2 n-k =ûú6 24ëê ùS2 +(K−3)2é) a - for which purposes in econometric applications of equations or equations mentioned below explain their use  = 1- (1-R 2 ) n-1 n-k = n

q23-  What is the aspect of sound regression analysis? Select one: a. Keep trying different models until statistical significance is achieved  b. Reporting only the results that are statistically significant c. Statistical significance solely based on "p-value < 0.05" d. Economic plausibility and significance of the model Clear my choice

Q5. Show that µY = Yµ − µY · 1. Data Mining Regression Evaluation chapter

Perform necessary tests and analysis to determine the validity of the regression attached in the below table and function provided The tests and analysis must be broken down into two sections namely: tests that are possible with the given regression’s information and tests that should be conducted but are not possible with the given information. For the tests that are possible please conduct them at a 5% significance level and for those that are not possible only mention their names without any further details

The following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ŷ = 21 + 13x1 + 9x2 The data used to develop the model came from a survey of 10 stores; for those data, SST = 19,000 and  SSR = 14,630. (a)For the estimated regression equation given, compute R2. R2 = ?? (b)Compute Ra2. (Round your answer to two decimal places.) Ra2 = ?? (c)Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.) The adjusted coefficient of determination shows that (??) % of the variability has been explained by the two independent variables; thus, we conclude that the model    does  explain a large amount of variability.

When the R2 of a regression equation is very high, it indicates that all the coefficients are statistically significant. the intercept term has no economic meaning. a high proportion of the variation in the dependent variable can be accounted for by the variation in the independent variables. there is a good chance of serial correlation and so the equation must be discarded.

Question 19 Marginal revenue (MR) is ____ when total revenue is maximized. Question 20 Even though insignificant explanatory variables can raise the adjusted R2 of a demand function, one should not interpret their effects on the regression when Question 21 The constant or intercept term in a statistical demand study represents the quantity demanded when all independent variables are equal to: Question 22 In regression analysis, the existence of a significant pattern in successive values of the error term constitutes: Question 23 Demand functions in the multiplicative form are most common for all of the following reasons except: Question 24 The standard deviation of the error terms in an estimated regression equation is known as: Question 25 In which of the following econometric problems do we find Durbin-Watson statistic being far away from 2.0? Part 2 Question 1 Which of the following barometric indicators would be the most helpful for forecasting future sales for an industry?…

The 2008 sales and profits of seven companies were given as follows Firm Sales ($ Billions) Profit ($ Billions) Fiat 5.7 0.27 Honda 6.7 0.12 BP 0.2 0.01 Toyota 0.6 0.04 Apple 3.8 0.05 IBM 12.5 0.46 Phillips 0.5 0.02 The estimated value for the company’s Profit can be estimated using the equation; Y ̂i = α ̂ + β ̂Xi……………………………………………………………………Eqn.1 Where; Y = Companies Profit X = Companies Sales α ̂ and β ̂ are estimated parameters in the model Calculate the sample regression line, where profit is the dependent variable (Y) and sales is the independent variable (X)

No written by hand solution Consider the following data: x⎯⎯x¯ = 20, sx = 2, y⎯⎯y¯ = −5, sy = 4, and b1 = 0.40. Which of the following is the sample regression equation?   Multiple Choice   yˆ = −13 − 0.40x   yˆ= −13 + 0.40x   yˆ = 3 − 0.40x   yˆ = 3 + 0.40x

True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.

Assume Demand equation of a product as Q = 70 -10 P + 4Pr + 50 I Where Q = Quantity of the product demanded, P = Price of the product (in $), Pr = Price of the related product (in $) and I = Per capital income (in ‘000)   State the key steps for analyzing the above demand equation and calculate the regression results. What are the implications of the above regression analysis for management decisions?

Consider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.