# Statistic assignment Essay Example

• Category:
Mathematics
• Document type:
Math Problem
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• Page:
2
• Words:
812
1. Price elasticity of demand Estimated elasticity of demand is 9.763 as can be seen from table 3. The 95% confidence interval of elasticity is 8.079 to 11.446 as shown in table 3. The p-value for Inprice is 0.000 which is a clear indicator that intuitively admissions are dependant on price.

 Model Summary Adjusted R Square Std. Error of the Estimate 223.56155 a. Predictors: (Constant), price
 Sum of Squares Mean Square Regression 3416083.497 3416083.497 Residual 49979.765 a. Predictors: (Constant), price b. Dependent Variable: admis
 Coefficientsa Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Std. Error Lower Bound Upper Bound (Constant) a. Dependent Variable: lnadmis
1. Addition of week, sequel , review and star variables

When the new variables are added the R2 value changes from 0.058 to 0.345 as seen from table 4. From table 6 it is clear that all the variables have coefficients which are statistically different from zero where all the p-values for the variables are 0.000 except for lnbudget. From the coefficients given in table 6 it can be seen that the price increase result a substantial decrease in attendance with a coefficient of -2.047. The week of release also contribute to the reduction of the number of attendance even though its contribution in reduction is weak, the coefficient being -0.282. The other three variables have positive coefficients and thus they contribute positively to the number of attendance where sequel has the highest coefficient of 1.259 followed by ‘star’ at 0.605 while review has a coefficient of 0.318.

 Model Summary Adjusted R Square Std. Error of the Estimate a. Predictors: (Constant), star, lnprice, review, lnbudget, sequa, week
 Sum of Squares Mean Square Regression Residual 1339.686 2046.367 a. Predictors: (Constant), star, lnprice, review, lnbudget, sequa, week b. Dependent Variable: lnadmis
 Coefficientsa Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Std. Error Lower Bound Upper Bound (Constant) lnbudget a. Dependent Variable: lnadmis
1. Effect of weekend on admissions

The weekends have a positive effect on admission as can be seen from the coefficients of Friday, Saturday and Sunday where Saturday has the greatest contribution with a coefficient of 0.46 while the coefficients for Friday and Sunday are 0.287 and 0.345 respectively. The overall effect is that the model has been strengthened as the R2 value has increased from 0.345 to 0.362 as observed in table 7.

 Model Summary Adjusted R Square Std. Error of the Estimate a. Predictors: (Constant), sun, sequa, friday, week, lnbudget, star, lnprice, sat, review
 Sum of Squares Mean Square Regression Residual 1306.582 2046.367 a. Predictors: (Constant), sun, sequa, friday, week, lnbudget, star, lnprice, sat, review b. Dependent Variable: lnadmis
 Coefficientsa Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Std. Error Lower Bound Upper Bound (Constant) lnbudget a. Dependent Variable: lnadmis
1. Effect of opening day, public holidays and school holidays

The three variables contributes to the admissions as can be seen from table 10 where R2 increased from 0.362 to 0.40 and also from table 11 it can be observed that F value has reduced and the model is statistically significant with p=0.000. From table 12 it can be seen that school holiday has the highest impact with a coefficient 0.540 at p=0.000, followed by opening day with a coefficient of 0.534 at p=0.014. The contribution of public holiday is not statistically significant at p=0.311. Thus the boss intuition was right for school holidays and opening day as they contributed to increase in admissions but public holiday did not contribute to increase in admissions

 Model Summary Adjusted R Square Std. Error of the Estimate a. Predictors: (Constant), school, lnbudget, open, sequa, sat, star, friday, review, lnprice, public, sun, week
 Sum of Squares Mean Square Regression Residual 1227.227 2046.367 a. Predictors: (Constant), school, lnbudget, open, sequa, sat, star, friday, review, lnprice, public, sun, week b. Dependent Variable: lnadmis
 Coefficientsa Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Std. Error Lower Bound Upper Bound (Constant) lnbudget a. Dependent Variable: lnadmis
1. Maxto and daily recorded rainfall

F2,1107 = = This has a p-value of 0.11 and thus the coefficients can be taken as zero.

 Model Summary Adjusted R Square Std. Error of the Estimate a. Predictors: (Constant), rain, public, sequa, open, maxto, lnbudget, star, review, sun, lnprice, school, friday, sat, week
 Sum of Squares Mean Square Regression Residual 1222.383 2046.367 a. Predictors: (Constant), rain, public, sequa, open, maxto, lnbudget, star, review, sun, lnprice, school, friday, sat, week b. Dependent Variable: lnadmis
 Coefficientsa Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Std. Error Lower Bound Upper Bound (Constant) lnbudget a. Dependent Variable: lnadmis
1. Using the model

Where y is Natural log of admissions (Inadmis) and the x’s are the statistically significant variables as shown in table 15 with their order of appearance being maintained

y = 11022 -2.66  y = 11.022 -2.66  admissions = 936 people.

1. Computing CI 936 =10.500 =1.05225 = 3.123 = 936 