1) For recommendations on which laptop to purchase, consumers look at the ratings provided by Consumer Reports. A sample of 12 laptops was selected and the rating and score on the laptops' features were recorded as shown in the ‘laptops' file. The description of the variables in the ‘laptops' file is as follows: model (brand and description of laptop), price (retail price of laptop), rating (overall score by Consumer Reports), and features (a score of 1, 2, or 3 with low values indicating more features).
a) Find the prediction equation for the price of a laptop using rating and features. What is the value of the residual standard deviation?
b) If the value of SSE were equal to zero for this problem what would that imply?
2) The following regression equation was calculated from a dataset of 20 observations: Yhat = -1.0 + 2.5X1 + 4.0X2. The value of MSR and MSE are .465 and .004 respectively. The standard deviations of the regression coefficients of X1 and X2 are .26 and .21 respectively.
a) Test the hypothesis that at least one of the regression coefficients is not equal to zero. Use a .05 significance level.
b) Test Ho: β1 = 0 versus Ha: β1 ¹0. Use a .05 significance level.
c) Test Ho: β2 = 0 versus Ha: β2 ¹0. Use a .05 significance level. Many chief executives have been under serious criticism from organized labor for the fat paychecks that they take home. An experiment was set up in which 15 observations were taken on the variables: Y = chief executives' pay (in thousands of dollars), X1 = firm's net profit (in millions of dollars), and X2 = number of employees (in thousands). Using excel, the following sample statistics were obtained: b1 = 0.1336, sb1 = 0.0424, b2 = -0.86, sb2 = 0.39.
a) Given that X2 is in the model, does X1 contribute to predicting the dependent variable at the .05 significance level?
b) Given that X1 is in the model, does X2 contribute to predicting the dependent variable at the .05 significance level?
3) The SSE and SST for a regression equation with three independent variables were found to be 26 and 250 respectively. The number of observations was 10.
a) Calculate the R2 value.
b) Calculate the adjusted R2 value.