## Using the variable “GDP per capita (constant 2010 US\$)” estimate the following (four points, round to two decimals) [R1] Mean, Median and Interquartile range

1) Using the variable “GDP per capita (constant 2010 US\$)” estimate the following (four points, round to two decimals) [R1]: a. Mean. b. Median. c. Interquartile range (IQR). d. Standard deviation. 2) Taking “Labor force growth (annual %)” as the response variable, and “GDP per capita growth (annual %)” as the predictor variable. Estimate the following (5 points) [R2]: a. Average labor force growth. b. Average GDP per capita growth. c. Sum of the cross products of the x deviations with the y deviations. d. Sum of the squared deviations of the x observations. e. Sum of the squared deviations of y observations. 3) Using only the results from the previous question, estimate the following (6 points) [R2]: a. The correlation between labor and GDP per capita (both annual growth). b. The slope (or beta.hat1), how do you interpret this value? c. The intercept (or beta.hat0). d. Sum of squares due to error. e. The variance of the regression. f. The R 2 of the regression, what is this number telling you? 4) Does GDP per capita have a significant effect on labor force? To answer this question, using previous estimates, calculate the following (3 points) [R2]: a. The standard error of the slope b. The t-value of the slope c. Can we say with 95% confidence that the effect of GDP per capita growth on labor force is significant (two-sided test)? Yes/No, and why? 5) Using two standard deviations and the variable “Household final consumption expenditure per capita growth (annual %)”, estimate the following (four points) [R1]: a. Upper control limit b. Lower control limit c. Which year or years, if any, were ‘out of control’ on the upper end? d. Which year or years, if any, were ‘out of control’ on the lower end? Econ Data Analytics – Summer 2018 – 01:220:212:H6 – Rutgers New Brunswick – OTR 6) Classify the years into three groups: group 1 will be from 1991 to 1999, group 2 from 2000 to 2009, and group 3 from 2010 to 2016. Now take the variable “Household final consumption expenditure per capita (constant 2010 US\$)”, estimate the following for this variable (7 points) [R2]: a. Average consumption between 1991 and 1999. b. Average consumption between 2000 and 2009. c. Average consumption between 2010 and 2016. d. The treatment sum of squares and its degrees of freedom. e. The error sum of squares and its degrees of freedom. f. The F-ratio. e. Can we say, with 95% confidence level, that household consumption has indeed changed over time; this is, is the mean consumption different across all three groups? Yes/No, and why? 7) Taking “Labor force growth (annual %)” as the response variable, “GDP per capita growth (annual %)” and “Trade (% of GDP)” as the predictor variables, run a multiple linear regression (you can use the Data Analysis ToolPak or lm() R function only for this question). Report the following (3 points) [R2]: a. The R 2 of the regression, what is this number telling you? b. The standard error of the regression, what is this number telling you? c. Based on the above results, comparing the models with and without trade (from questions 3 and 4), which one would you say has more explanatory power and why?