Business Statistics

Bob wants to construct a linear regression model to examine whether there is any relationship between the income and race of working adults in Singapore.

He records the race of a person as chinese, malay, indian or others. He uses data from a simple random sample of 30 working adults to building the following details model.

Income ($ per month) = A + B x I Malay + C x I Indian + D x I others. Where A, B, C and D are the coefficients and I Malay = if person malay otherwise, I Indian = if person Indian otherwise, and I others = if person Others otherwise. He uses SPSS to evaluate the details model and estimate the coefficients using the data. The following is the output. For ANOVA, sum of squares for regression is 32765441.887, sum of squares for residual is 83761696.062, and sum of squares for total is 116527137.949. The df and mean square, and F statistic for regression, residual, and total is unknown. The significance level for regression is 0.033. The significance level for residual and total is unknown. The following is Coefficients. (Constant) for unstandardised coefficients is 7502.621, I_Malay for unstandardised coefficients is -2029.020, I_Indian for unstandardised coefficients is 518.665, and I_Others for unstandardised coefficients is 1472.207. The standard error for (Constant) is 463.437, standard error for I_Malay is 926.873, standard error for I_Indian is 926.873, and standard error for I_Others is 926.873. (Constant) for standardised coefficients is unknown, I_Malay for standardised coefficients is -0.384, I_Indian for standardised coefficients is 0.098, and I_Others is 0.278. (Constant) for t statistic is 16.189, I_Malay for t statistic is -2.189, I_Indian for t statistic is 0.560, and I_Others for t statistic is 1.588. (Constant) for significance level is 0.000, I_Malay for significance level is 0.038, I_Indian for significance level is 0.581, and I_Others for significance level is 0.124. Bob conduct the F statistic test at the 5% significance level to determine whether there is any relationship between the variables in the model.

Calculate degree of freedom on the numerator for the F statistic. Calculate the degree of freedom on the denominator for the F statistic. What is the critical value of the F statistic. What is the conclusion for this F statistic test and provide 3 reasons for null hypothesis should be rejected or should not be rejected. Calculation and workings must be have clear and final answer must be rounded off to 3 decimal places when appropriate.

Calculate the income that the details model would predit for chinese working adult and malay working adult, and for Malay working adult. Calculation and workings must be have clear and final answer must be rounded off to 2 decimal places when appropriate.

At the significance level, is there evidence of a difference in incomes between Indian and Chinese working adults on average. What are the 3 reasons for yes/no for is there evidence of a difference in incomes between Indian and Chinese working adults on average by clearly referring to the appropriate p-value in the SPSS output.