ECON7300: Statistical Project Assignment 代写

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ECON7300: Statistical Project Assignment 代写

ECON7300: Statistical Project Assignment, Semester 2, 2017

Instructions for Dataset3: Simple Regression Analysis (Weighting: 12%)

Shoe size generally is proportional to height. Someone might ask: Is there a relationship

between shoe size and height? To answer this questions a random sample of 153

students at a large university were surveyed and asked each student to report their

shoe size and height. Data for this is stored in Dataset3.

The variables in Dataset3 are:

 Shoe size (X, in EU size)

 Height (Y, in cm)

The dependent variable for your analysis is Height.

Answer the following questions using Dataset3.

(a) Estimate a regression model using X to predict Y (state the simple linear

regression equation).

(b) Interpret the meaning of the slope.

(d) Compute the coefficient of determination and interpret its meaning.

(e) Compute the standard error of the estimate and interpret its meaning. Judge the

magnitude of the standard error of the estimate.

(f) Perform a residual analysis (plot the residuals) and evaluate whether the

assumptions of regression have been violated.

(g) Test for the slope using t test (follow all the necessary steps). Assume 5% level

of significance.

ECON7300: Statistical Project Assignment 代写

(h) Test for the slope using F test (follow all the necessary steps). Assume 5% level

of significance.

(i) Test for the correlation coefficient (follow all the necessary steps). Assume 5%

level of significance.

(j) Compute a 95% confidence interval estimate of the mean Y for all students (at a

large university) when X = 38 and interpret its meaning.

(k) Compute a 95% prediction interval of Y for an individual student (at a large

university) when X = 38 and interpret its meaning.

ECON7300: Statistical Project Assignment, Semester 2, 2017

Instructions for Dataset 6: Multiple Regression Analysis (Weighting: 18%)

The dataset (n = 1900) is an extract of the US National Longitudinal Survey for

employed women in 1988. Data for this is stored in Dataset6.

The variables in the dataset are:

 wage (Y, hourly wages in dollar)

 grade (X1, current grade completed by the employee)

 hours (X2, number of hours worked per week)

 south (X3, coded1 if the employee lives in south and 0 otherwise)

The dependent variable for your analysis is wage.

Answer the following questions using Dataset6

(a) Estimate a regression model using X1 and X2 to predict Y (state the multiple

regression equation).

(b) Interpret the meaning of the slopes.

(d) Compute a 95% confidence interval estimate of the mean Y for all employed

women when X1 = 10 and X2 = 38 and interpret its meaning.

(e) Compute a 95% prediction interval of Y for an employed woman with X1 = 10

and X2 = 38 and interpret its meaning.

(f) Plot the residuals to test the assumptions of the regression model. Is there any

evidence of violation of the regression assumptions? Explain.

(g) Determine the variance inflation factor (VIF) for each independent variable (X1

and X2) in the model. Is there reason to suspect the existence of collinearity?

(h) At the 0.05 level of significance, determine whether each independent variable

(X1 and X2) makes a significant contribution to the regression model (use t tests

and follow all the necessary steps). On the basis of these results, indicate the

independent variables to include in the model.

(i) Test for the significance of the overall multiple regression model (with two

independent variables, X1 and X2) at 5% level of significance.

(j) Determine whether there is a significant relationship between Y and each

independent variable (X1 and X2) at the 5% level of significance (hint: testing

portions of the multiple regression model using the partial F test).

ECON7300: Statistical Project Assignment, Semester 2, 2017

(k) Compute the coefficients of partial determination for a multiple regression model

containing X1 and X2 and interpret their meaning.

(l) Estimate a regression model using X1, X2 and X3 to predict Y (state the multiple

regression equation, the regression equation for employees living in south, the

regression equation for employees not living in south) and interpret the

coefficient for X3.

(m) Estimate a regression model using X1, X2, X3, an interaction between X1 and

X2, an interaction between X1 and X3, and an interaction between X2 and X3 to

predict Y.

(n) Test whether the three interactions significantly improve the regression model.

Assume 5% level of significance (hint: test the joint significance of the three

interaction terms using the partial F test. If you reject the null hypothesis, test the

contribution of each interaction separately (using the partial F test) in order to

determine which interaction terms to include in the model).

ECON7300: Statistical Project Assignment 代写