Assignment 4 Instructions: This assignment is due March 4th by midnight. Please submit through Canvas! Do not email your assignment. You may work and submit in pairs. A single file with both students will suffice. If you submit different files and worked in pairs, make sure to add the name of the person who worked with you. 1. Americans were asked in 1971 to rank themselves on a "happiness index as follows: H=0 (not happy), H=1 (fairly happy), or H-2 (very happy). Annual household income (in thousands) was recorded for each individual (X). The table below shows the proportions of various levels of H and X. Use these values to calculate: a. The expected value of X and the one of Y. b. E(H|X=2.5), E(H|X=17.5), E(X|H=0) c. The covariance of X and H d. The correlation coefficient between X and H h 2.5 7.5 12.5 17.5 0 0.03 0.02 0.01 0.01 1 2 0.12 0.07 0.13 0.11 0.13 0.14 0.09 0.14 Note: For simplicity, do not convert the income variable to thousands. 2. The table below shows results on a survey of 693 zip codes. All zip codes are in urban areas with low to middle income households. Researchers wanted to assess the relationship between income and number of fast food restaurants as part of a project to assess the determinants of quality of calorie intake. The columns show the median income per zip code and the rows show the number of fast food restaurants. Inc-Median income per zip code FFR = #fast food 32 38.5 40.2 45 52 58 63 72 restaurants 1 1 3 4 2 4 5 6 3 10 12 16 4 18 16 5 19 21 14 6 21 17 17 7 36 36 18 109 110 91 424252280 16 1 6 6 12 16 16 12 14 26 21 18 7 28 7 38 10 81 13 130 22 24 22 7 147 15 9 5 5 6 94 9 9 12 6 66 4 4 205 85 118 88 94 84 72 45 693 Using the information above find: a. The average household income in the sample. b. The average number of fast food restaurants found. c. The average income for zip codes with 1, 5 and 7 fast food restaurants (this would be the conditional expected value of income for each value of FFR). What do you observe? d. The covariance and correlation coefficients