Use the dataset that you have been using for the previous projects.

Use all of your independent variables, your response variable, and the lm() function to build a multiple linear regression model.

Print the model with the summary() function. The output will be similar to the bottom of page 141.

Use the pairs() function to look at the scatterplots of the interval/ratio variables. Color your points by the value of a nominal/ordinal variable.

A standard regression model with correlated independent variables will almost always perform poorly. For this project, you will remove independent variables until the model is trustworthy.

Use the summary() output, and the scatterplots to decide if a variable should be removed. Remove the variable.

Repeat the process of

• build model

• check summary() and scatterplots

• remove variable

until you believe all variables in the model should stay in the model.

Use par(mfrow = c(2,2)) and the plot() function to look at diagnostic plots of the reduced model (similar to the plots on page 129).

Grading criteria:

• full model

• summary()

• pairs()

• remove independent variables, print reduced model each time (60% of grade)

• plot() final model

Create a simple linear regression model with one of your numeric independent variable and your response variable.

Build the scatterplot of the response variable by the independent variable, and the scatterplot of the residuals by the independent variable (similar to figure 3.3, page 50). Include the line of best fit on the first scatterplot. Also, plot the residuals by the response variable. Do you the scatterplots indicate that there are any problems with the model?

Use hist() to plot a histogram of the residuals. Do the residuals appear to be normally distributed?

Use qqnorm() and qqline() to plot a QQ-normal plot with the QQ-line of the residuals. Do the residuals appear to be normally distributed?

Use par(mfrow = c(2,2)) and plot(‘linear model’) to build a plot similar to figure 3.14 on page 70.

Record which data points are labeled in the subplots, then print those observations. Investigate each of these points and decide which ones are legitimate data points and which ones are erroneous and polluting your dataset.

Use car::powerTransform() to find power transformations for

• y – min(y) + 1, and

• x – min(x) + 1.

Transform the data and call the new data y_new and x_new. Build four scatterplots.

• y ~ x

• y_new ~ x

• y ~ x_new

• y_new ~ x_new

Which of these models appears to be the be fit? Build the corresponding linear model.

Grading Criteria:

• Simple linear regression model (no transformations)

• Scatterplot y ~ x

• Scatterplot residuals ~ x

• Scatterplot residuals ~ y

• hist(residuals)

• QQ-norm plot

• Linear model four plots

• Leverage data

• Four post-transformation scatterplots

• New linear model

Sample Solution

Developing countries have been able to achieve improved productivity and specialization through adoption of technologies that have been introduced in their countries by other developed countries through trade liberalization. For example, India has evidenced comparative advantage by employing labour intensive production skills in manufacturing and services that employs intensive skills as in software industries. This has led to its increased exports in its production to other Asians countries thus increasing its revenues and gross domestic income that has played a major role in its economic development. High technologies attract foreign investors and investments increase. Increased investments in the developing countries also results to significant decrease in levels of unemployment. Consecutive increase in exports from developing countries has been due to decreased barrier and reduced tariffs (Johnston, et al 2011, free trade). Therefore, it can be concluded that free trade is has helped countries to advance economically and realise their economic goals such as millennium development goals. Free trade has led increased access of economic resources to developing countries and utilization of limited available resources thus stimulating their economic and social development. Small developing countries struggle with scarce and underutilised resources. Free trade allows free entry of other countries and investors to small developing countries and as a result, they participate in conversation of the available resources to economic development resources through ‘mobilization of capital and labour thereby improving the status of the country in the economy’ (Unger, 2010 P 171). Moreover, free trade gives small developing nations chances to obtain resources such as capital from already developed countries that assist them to attain economic development resources or utilize what they have. For example, countries from Asia such as India have developed due to trade liberalization where they have been able to obtain capital, labour and other necessary resources from already dev>

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