STA 510 Business Statistics - Assignment
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Added on 2021-05-31
STA 510 Business Statistics - Assignment
Added on 2021-05-31
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STA 510 Business StatisticsSemester 1, 2018Assignment 2SolutionQuestion 2a)Based on the regression output we have to find out the trend equation and interpret. Now, from the output we get that it is an output of a simple linear regression i.e. there is only one response variable and only one independent variable. Here the response variable is goggle sales(in thousands of dollars) denoted by “y” and the independent variable is time variable denoted by “t”. Here the origin of the data is the march quarter 2000.Here the coefficient of intercept is 12.237 and the coefficient of the time variable is 0.26289.So the trend line is, y(in thousands of dollars)=12.237+0.26289 t (Origin: March Quarter 2000)Interpretation: Hence for each unit increase in the time variable t i.e for each quarter from march quarter 2000 there will be an increase of 0.26289 unit in the goggle sales (in thousands of dollars).b)95% Confidence interval of the variable is given by,(0.080812368,0.4449738) According to the confidence interval if we collect samples again and again from the population again and again then 95% of the times the coefficient of time variable t will lie within this interval i.e for each unit of increase in the time variable t there will be an increase in the responsevariable i.e in the goggle sales (in thousands of dollars) will lie within the interval (0.080812368,0.4449738) .
c)Management report about forecast of goggle sales of each quarter of 2016Introduction:According to the researcher’s problem a company which is selling swimming goggles desires to investigate the company’s Australian sales. Dataset of 54 observations were collected and based on that a time series forecasting model using Regression technique was used. Our main aim is to forecast sales of goggle sale in the upcoming years.Here, the data was used to generate Excel output using the Excel Data analysis function to generate the summary output and from the summary output we are able to estimate trend of the time series of Swimming goggle sales. Here the unit of sales taken is in thousands of dollars. We have made the origin of the data as March Quarter 2000. In this way we have changed the data “t” in such a way that the origin of “t” is in March Quarter 2000. So, the data observed in 2000’s second quarter is t=1,third quarter t=2... and so on. Our motivation is to find out how the sales of swimming goggle depend in the time variable i.e. the degree to which the sales are predicted by the year. Another aim is to forecast or predict the number of sales in the upcoming years. This is done by many companies so that they could knowhow much products to be manufactured so that they are on the profit side. At first we have found out the correlation i.e. the association among the two variables . Then we have done a regression analysis along with its anova table is given from which we have got full information about the data which helps us to predict the goggle sales in the future quarters. We have used regression analysis and one way anova . Here our dependent variable is Goggle sales and independent variable is Year. We have here considered only simple linear regression.Output and Interpretations: From the data, Using Excel we get the following results using “Data Analysis” Tool in Excel.Regression Output:The following table gives the regression parameters’ coefficients, t statistic value and p value associated with them . Also the 95% upper and lower confidence intervals are also given.CoefficientStandard ErrorT statisticP valueLower 95%Upper 95%intercept12.2372.78964.395.6E-056.6417.83t0.2620.09072.8970.00550.08080.445Formula:Independent Variable: XOutput Variable: YNumber of Observation: n
Correlation Coefficient = ∑(Xi¿− ́x)(Yi− ́y)√∑(xi− ́x)2∑(yi− ́y)2¿= RCoefficient of Determination= R2T statistic =^βiS.E.(βi)Table 1: Table showing Regression Parameters and their properties of Google sales vs YearHere, Multiple correlation coefficient R=0.37281R(square) or Coefficient of Determination= 0.13899Adjusted R square=0.12243 Standard Error=10.3925The Anova Table:DfSum of SquaresMean Sum ofSquaresF statisticSignificnce FRegression1906.5867925906.598.394060.005497292Residual525616.172467108--Total536522.759259---Table 2: Table showing Anova table associated with the regression of Google sales vs YearInterpretation of Correlation Coefficient:Here, the correlation coefficient is given as 0.37281. Hence there is a positive trend in the data astime increases the goggle sales will increase. It implies the company is running in profits. Interpretation of standard Error:Here in the regression output we get the standard error which is associated with the regression problem. This can be used to evaluate the accuracy of the forecasts. Standard error is used mainly to compute the accuracy of the forecasts as with the help of it we can get the limit in which the 95% of the values should lie . It gives the interpretation that they should lie inside ±2*Standard Error of the regression. In this way we can quickly deduce an estimate of the prediction interval precisely 95%. As the standard error is 10.3925 so the prediction interval will be ±2*10.3925 From the above table we get the coefficients of intercept and t variable. P values associated with them is less than 0.05(significance level) which implies the regression is significant. Interpretation of the confidence intervals of the coefficients of “t” and intercept: As the confidence interval of intercept is (6.64,17.83) i.e. it does not contain 0 so it is significant. On the other hand confidence interval of coefficient of “t” is (0.0808,0.445) so it does not contain 0 hence it is also significant. Adjusted R square take into account the number of predictors. It penalizes for adding number of predictors.
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