HW11_solution

CEE 373 Homework #11 Due date: December 6 at 11:59pm (NOTE: Wednesday due date) Total: 100 points (NOTE: This HW will replace your lowest HW score) 1. (25 points) Data for the per capita energy consumption and per capita Gross Na- tional Product (GNP) for eight different countries have been compiled by Mead- ows et al. (1972) and tabulated below. Table 1: Country-wide energy consumption and GNP for eight countries Country Per Capita Gross National Product, X Per Capita Energy Consump- tion, Y 1 600 1000 2 2700 700 3 2900 1400 4 4200 2000 5 3100 2500 6 5400 2700 7 8600 2500 8 10300 4000 Please answer the following questions using this data. (a) Plot a scatterplot of Y versus X (b) Determine the linear regression equation for predicting the per capita energy consumption ( Y ) on the basis of a country’s per capita GNP ( X ) and plot the regression line with your scatterplot from part (a). Please calculate regression coefficients by hand (you may check your answers with Python or another computing software). (c) Determine the the R 2 value. What does the R 2 value tell you about the appropriateness of the fit of this linear regression equation? (d) Estimate the Per Capita Energy Consumption for a new country whose Per Capita GNP is 200. Solution: Refer to the solution code https://colab.research.google.com/drive/ 1HGiiJzofZhQWvip5SwAAz5jhDBXRVrdz?authuser=0#scrollTo=g2acxo7tulJU . Page 1 of 8

CEE 373 Homework #11 (a) Scatter plot (b) From the data, the mean values of X ( X ) and Y ( Y ) are: X = 4725 . 0 Y = 2100 . 0 When you calculating regression coefficient ( ˆ β 1 ) and intercept ( ˆ β 0 ), ˆ β 1 = ∑ n i =1 ( x i − x )( y i − y ) ∑ n i =1 ( x i − x ) 2 = 0 . 279 ˆ β 0 = Y − ˆ β 1 X = 783 . 15 Thus, the fitted regression line is: ˆ Y = ˆ β 0 + ˆ β 1 X = 783 . 15 + 0 . 279 X When you draw the regression line with the scatter plot: Page 2 of 8