Question

In: Statistics and Probability

Assume the following time series regression has been estimated for sales of gadgets: St = 20...

Assume the following time series regression has been estimated for sales of gadgets:

St = 20 + 13Q1 + 9Q2 +4Q3 + 2t + 3t2;

where t is the time trend and Q1, Q2 and Q3 are dummy variables for quarters 1, 2 and 3

respectively. Assume the data used in the regression starts in the first quarter of 2016 and ends

in the first quarter of 2018. Forecast the expected sales for quarters 2, 3 and 4 of 2018.

Expert Solution

Assume the following time series regression has been estimated for sales of gadgets:

St = 20 + 13Q1 + 9Q2 +4Q3 + 2t + 3t2

where t is the time trend and Q1, Q2 and Q3 are dummy variables for quarters 1, 2 and 3

respectively. Assume the data used in the regression starts in the first quarter of 2016 and ends in the first quarter of 2018. Forecast the expected sales for quarters 2, 3 and 4 of 2018.

Understanding the dummy variable

Dummy variable for Q1, if the Quarter is 1, then Q1 = 1 or Q1 = 0

Dummy variable for Q2, if the Quarter is 2, then Q2 = 1 or Q2 = 0

Dummy variable for Q3, if the Quarter is 3, then Q3 = 1 or Q3 = 0

The trend (t) is shown below

Forecast for 2018 - Q2

Q1= 0
Q2 =1
Q3 = 0
t = 10

Regression equation

Forecast for 2018 - Q3

Q1= 0
Q2 =0
Q3 = 1
t = 11

Regression equation

Forecast for 2018 - Q3

Q1= 0
Q2 =0
Q3 = 0
t = 11

Regression equation

orchestra answered 2 years ago

In a time-series decompostion of sales (in millions of units), the following trend has been estimated:...

In a time-series decompostion of sales (in millions of units), the following trend has been estimated: CMAT=12.315+0.196(T) The seasonal indices have been found to be: Quarter Seasonal Index 1 1.27 2 1.02 3 0.73 4 0.98 For the coming year, the time index and cycle factors are: Quarter T CF 1 21 1.01 2 22 1.04 3 23 1.06 4 24 1.04 a. From this information, prepare a forecast for each quarter of the coming year. b. Actual sales for...

Consider the following quarterly time series. The regression model developed for this data set that has...

Consider the following quarterly time series. The regression model developed for this data set that has seasonality and trend is as follows, yˆt = 864.08 + 87.8Qtr1t + 137.98Qtr2t + 106.16Qtr3t + 28.16t Compute the quarterly forecasts for next year based on the regression model? Quarter Year 1 Year 2 Year 3 1 923 1112 1243 2 1056 1156 1301 3 1124 1124 1254 4 992 1078 1198

Consider the following regression results of B for time series data. The dependent variable is the...

Consider the following regression results of B for time series data. The dependent variable is the log of real consumption and the regressors are all lagged by one period. The coefficients are estimated by OLS method. *, **, and *** indicate that the coefficients are significant at the 10%, 5%, and 1% level, respectively. The F- test in the last row tests the joint hypothesis that all the coefficients except the constant are zero and their p-values are provided in...

The following Regression function has been developed to check the relationship between Y- ‘Sales’ and the...

The following Regression function has been developed to check the relationship between Y- ‘Sales’ and the following independent variables; X1- Time (Length of time employed in months) X2 –Poten (Market potential) X3 – AdvExp (Advertising expenditure in the sales territory) X4 – Accounts (Number of accounts assigned to sales rep) 3 Consider the following Minitab output and answer the questions. Regression Analysis: Sales versus Time, Poten, AdvExp, Accounts Regression Equation Sales = -391 - 0.58 Time + 0.02227 Poten +...

Following is an Estimated Multiple Regression for Cigaretteconsumption in the US. Based on the estimated...

Following is an Estimated Multiple Regression for Cigarette consumption in the US. Based on the estimated parameters, and other statistics, Answer the following questions:CigaConsm = 14.5 + 0.06LnInc – 0.65LnCigPr. + 0.025LnExcTax + 0.034GenderT-stats: (2.90) ( 1.30) (-2.25) (2.40) (1.67)Where CigaConsm represents cigarette consumption in millions of boxes per year in a given state; Inc is median household income of the State; Cigpr is cigarette price per pack; Exctax is Excise tax per pack of Cigarette,...

Suppose that the demand (sales) function for a product A has been estimated as: ? =10.5−.8?...

Suppose that the demand (sales) function for a product A has been estimated as: ? =10.5−.8? −.2? +.1? +.0005? ? ??? Where, ?? is the quantity of product A demanded, in thousand per month. ? is the price of product A; ? is the price of product B, which is currently $10; ? ? is the price of product C, which is currently $5; and ? Y is the level of per capita income, which is currently $10,000. 1. Of...

Assume one has estimated a regression equation of salary (dependent variable) against years of education independent...

Assume one has estimated a regression equation of salary (dependent variable) against years of education independent variable). How would one go about expanding the regression model to also estimate the gender effect (i.e., the average difference between male and female salary, given the same level of education? Explain how you would construct the additional variable and how you would interpret it, given how you construct it. How would you construct a hypothesis test to determine if the estimated gender-based differential...

A series of 20 samples of size 4 has been drawn from a project. The measure...

A series of 20 samples of size 4 has been drawn from a project. The measure of interest has an average of 20.0443, and the average range within the samples is 0.0567. Determine the control chart lower limit for x-bar" "A series of 20 samples of size 4 has been drawn from a project. The measure of interest has an average of 20.0443, and the average range within the samples is 0.0567. Determine the control chart upper limit for R"...

Quarterly billing for water usage is shown below. Assume the time series has seasonality with a...

Quarterly billing for water usage is shown below. Assume the time series has seasonality with a long term trend. Year Quarter 1 2 3 4 Winter 64 66 68 73 Spring 103 103 104 120 Summer 152 160 162 176 Fall 73 72 78 88 Forecast the next four quarters: FWinter = 81.625, FSpring = 126.375, FSummer= 175.375, FFall= 92.625 FWinter = 80.625, FSpring = 120.375, FSummer= 175.375, FFall= 90.625 FWinter = 82.625, FSpring = 120.375, FSummer= 174.375, FFall= 90.625...

The following regression model has been proposed to predict sales at a computer store. Y=60-2X1+3

The following regression model has been proposed to predict sales at a computer store. Y=60-2X1+30X2+10X3 Where X1= competitor’s previous day’s sales (in $1,000s) X2=population within 1 mile (in 1,000s) X3= 1 if radio advertising was used; 0 if otherwise What is the estimated regression equation if no radio advertising was used? What is the estimated regression equation if radio advertising was used? What is the expected amount of sales attributable to radio advertising? Y=...