Business Statistic Assignment (Solution)

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Added on 2020-12-24

Business Statistic Assignment (Solution)

Added on 2020-12-24

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Business statistic

Table of ContentsQUESTION 2...................................................................................................................................3(a) Standard Error of Estimate:...............................................................................................3(b) Coefficient of determination:............................................................................................3(c) Adjusted coefficient of determination for degree of freedom:.........................................4(d) Overall Utility Level of Model:........................................................................................4(e) Interpretation of the coefficients:......................................................................................5(f) Relationship between heights of sons and Fathers:...........................................................6QUESTION 2(a) Standard Error of Estimate:The standard error of estimation is an estimated standard deviation of the error term “u”.It also known as standard error of the regression. Standard Error of Estimate is shows variation

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of observations. It is applied to inspect the accuracy of estimation made. Standard error ofestimate tells the accuracy of the estimated figures. Formula of standard error of estimate : sqrt(SSE/(n-k))Following is the calculation of Standard Error of Estimate:SSE25843.41k2n400N-k398SSE/(n-k)64.9331909548sqrt(SSE/(n-k))8.058113362The standard error should be low. The smaller the error, the meaningful the data. Suchdata represent the mean which should be considered as a standard and beyond which the datawill have characteristics of notable irregularities.(b) Coefficient of determination:The coefficient of determination is a measure used in statistical analysis that assesseshow well a model explains and predicts future outcomes. It shows the level of related variabilityin the data set. The coefficient of determination refers to R-squared and applied to determinecorrectness of the model. Coefficient of determination tells that variables in given model iscertain percentage of observed variation. It is represented as a value between 0 and 1. Closer thevalue is to 1, the better the fit, or relationship, between the two factors. Thus, in case the RSquare is equal to 0.2672, then approximately less than half of the observed variation can beexplained by the model.Formula of Coefficient of determination: MSS/TSS = (TSS − RSS)/TSSFollowing is the calculation of Coefficient of determination:TSS35264.98RSS25843.41TSS-RSS35264.98-25843.41 = 9421.58(TSS − RSS)/TSS9421.58/35264.98 Coefficient of determination 0.26716505Where MSS is the model sum of squares, RSS is the residual sum of squares and TSS isthe total sum of squares associated with the outcome variable. Above calculation shows r2=0.27means 27% of the variability in height of son's can be explained by differences in father’s height(x1) and mother’s height (x2).

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Business Statistic Assignment (Solution)