ever, you doubt the importance of the variable age. You are not sure what kind ofmarginal relationship is between age and the response ln(eval), given that beautyis already included in the model. Generate an appropriate plot to visually check thisrelationship and comment on the plot. Then conduct a partial F-test to determinewhether age is a significant addition to a model that already includes beauty.(f) [8 marks] The administrators remind you that a native English speaker and a nonnative English speaker tend to have a different eval. Therefore, you want toknow how does the variable native affect the response ln(eval). Conduct a testof whether a native English speaker has higher eval than a non-native Englishspeaker by fitting a simple linear regression model. Then provide a 95% confidenceinterval on the slope coefficient and interpret this interval.(g) [6 marks] Finally, given above findings, you decide to fit a MLR model with ln(eval)as the response variable and with beauty and native as predictor. Conduct a t-testfor beauty in this model.(h) [16 marks] Using the model in part (g), produce a plot of externally studentizedresiduals against fitted values, a normal QQ plot, a leverage plot, a Cook's distanceplot and a number of DFBETAs plots for all the slope coefficients in your model.Comment on the model assumptions and unusual points.(i) [8 marks] Generate a scatter plot of eval (in its original scale) against beauty,using different color for native and non-native speaking instructors. Use the modelfrom part (g) to predict the expected eval for both native and non-native speakinginstructors over the full range of possible beauty measurements and include theseon your plot as two different curves (using different color or line types). Includeappropriate titles, axis labels, a legend and a brief discussion of your plot.(j) [10 marks] With the model in part (g), we now consider adding the interactionterm between beauty and native. Before adding the interation, generate a scatterplot of ln(eval) (in log scale) against beauty, using different color for native andnon-native speakers. Add fitted lines (using the model in part (g)) for native andnon-native speakers in a different color (or a different line type). Comment on theplot whether there is a visible interaction. Then add the interation into the modelin part (g) and test whether the interaction is significant.