Use the following multiple regression model to explore the relationship of workers' earnings with variables related to sector, gender, educational attainment, age and marital status Model B: ????? = ?? + ???????? + ?????? + ? Model C: ????? = ?? + ???????? + ?????? + ????? + ? Model D: ????? = ?? + ???????? + ?????? + ????? + ??????????? + ? Model E: ????? = ?? + ???????? + ?????? + ????? + ??????????? + ?? ??????? + ?

a) Based on the Excel regression outputs, select the best model and explain why it is the best. b) Write down the estimated equation for the best model and interpret the slope coefficients, c) Based on the best model, carry out any relevant two-tailed hypothesis tests for each individual slope coefficient using the p-value approach, at the 5% significance level. d) Carry out an overall significance test using the p-value approach. e) Carefully interpret your hypothesis test results in c) and d).

1 gender age wage degree married public degree male married 2 Female 45 20.59375 No No H 3 Female 23 21.28125 No No 4 Male 44 22.5 No Yes Female 27 22.91667 Yes No 6 Male 28 23.10526 No No 7 Female 24 23.29545 No No 8 Female 31 23.34 Yes No 9 Male 28 24.23684 Yes No 10 Female 39 25 Yes Yes 11 Female 22 26.31579 Yes No 12 Female 27 27.77778 Yes No 13 Female 64 28.57143 No No 14 Female 44 29.22222 Yes No O H O H H O OHH O O O O O O O O H O O O O O HO O H HOO HOO HOOOOHHOP PPP POOPOOO HOHOOOHHPOPOOOOOOOHOOHOOO 15 Female 25 29.25 Yes No 16 Female 22 30.66667 No No 17 Male 28 30.66667 No No 18 Female 27 30.85 No No 19 Male 54 30.90909 No Yes 20 Male 45 31.25 Yes Yes 21 Male 28 31.875 No No 22 Female 46 32.43243 No No 23 Female 43 33.575 Yes Yes 24 Female 61 33.625 No Yes 25 Male 38 33.75 No No 26 Female 26 34 Yes Yes 27 Male 30 35.54054 Yes No28 Male 28 35.71429 No No 29 Female 28 35.76923 Yes No 30 Female 34 35.97368 No Yes 31 Female 25 36.43333 No No 32 Female 32 36.64444 Yes Yes 33 Male 48 37.21053 No No 34 Female 24 37.25333 Yes No 35 Female 29 37.33333 No No 36 Male 41 37.48889 Yes Yes 37 Female 37 37.5 Yes Yes 38 Female 57 37.5 No Yes 39 Male 32 39.47368 No No 40 Male 31 39.8 Yes No 41 Male 31 40 No No OOOH H H O H O H H O H OO OHH H OOOH OHOO HHOP HOHO HOHOOHH HOOHOOHOOOOL HOOP POP POO POO O HOOP HOHOHOOKO 42 Female 51 40.54054 No Yes 43 Female 32 41.09524 No No 44 Male 33 41.225 Yes Yes 45 Female 45 41.36666 No Yes 46 Male 53 41.6 No No 47 Female 32 42.13158 Yes Yes 48 Male 63 42.42424 Yes No 49 Female 46 43.05 No Yes 50 Male 58 45.13044 Yes Yes 51 Male 30 45.94 Yes Yes 52 Female 29 46.24 No No 53 Male 46 47.5 No No 54 Male 40 47.67442 Yes No55 Female 52 47.71111 Yes No O 56 Male 39 48.125 Yes No 57 Male 65 49.47368 No Yes 58 Male 59 50 No No 59 Male 40 50 Yes Yes 60 Male 57 50 No No 61 Male 26 50.35 Yes Yes 62 Male 37 50.875 Yes No 63 Female 31 51.35135 No Yes 64 Male 44 51.45 No No 65 Male 44 52.5 No No 66 Female 31 52.63158 Yes No 67 Female 31 52.75 Yes Yes 68 Female 55 54.6 Yes Yes 69 Female 41 55.55556 No No 70 Female 60 55.59459 Yes Yes O H O O H H O O H H O O O H H H O H H O O O H O H O H O H O O 71 Female 31 55.66667 Yes Yes HOWPHPOP POP POOOOOOOPPOPPPPP 72 Female 51 56.52632 Yes Yes 73 Male 39 57.14286 Yes No 74 Male 40 57.76 No No 75 Female 30 57.86842 No No 76 Male 33 58.05263 No Yes OOOH HOO OPPI 77 Male 38 58.45238 Yes Yes 78 Female 36 61.36666 Yes No 79 Male 53 62.3 No No 80 Male 56 64.47369 No Yes 81 Male 48 64.48 No Yes 82 Male 54 64.7 Yes No 83 Female 49 64.725 Yes No 84 Male 55 67.65455 Yes Yes 85 Male 60 78.91428 Yes No86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 Female Male Male Male Female Female Male Female Female Male Male Female Male Female Female Female Female Female Female Male Male Female Female Female Male Female Female Female Male Female Male 43 56 36 61 25 22 23 27 27 21 21 31 27 41 26 31 23 28 63 24 52 27 27 49 47 43 31 27 27 60 52 82.89474 Yes 98.975 Yes 3.009027 Yes 6.521739 No 9.2 No 10 No 10.56 No 13.5 Yes 14.58333 No 16.26667 No 16.42857 No 17.5 No 18 No 18.2 Yes 18.34211 No 19.18 No 19.18182 No 19.67442 No 19.90625 No 19.98333 No 20 No 20.18421 Yes 20.83333 No 21 No 21.4 No 21.4186 Yes 21.48889 Yes 21.5 Yes 21.81818 No 21.90476 No 22 No Yes Yes Yes No No No No No Yes No No No No Yes Yes No No Yes No No No No Yes Yes No No No Yes No No No DDOODDDODDODDDODDOODDOODDOODDHH DDOHHHOODHODDDODDHODDOOHDOODHH|-' I-lOI'OOOI'OOOHHOOOOOOHOHHOOHOOHHHO DOOHOOOHHOOOOHOOHHOOOOHOOOOOHHH 117 Male 22 22.275 No No 118 Male 22 22.5 No No 119 Male 60 22.63158 No No 120 Female 41 22.64151 No Yes 121 Male 39 23.08 No No 122 Female 39 24.56 No Yes 123 Female 48 24.57143 No Yes 124 Male 30 24.95 No Yes 125 Male 22 25 No No 126 Male 26 25.56667 Yes No 127 Male 22 25.66667 No No 128 Male 32 26 No No 129 Female 46 26.24 No Yes 130 Female 47 26.31579 No No 131 Male 31 26.90476 No Yes O O P O O P O P P O O P O O O O O O O H OOO OOO OOO O H O H O O O O O O O H O O H H H O H O O O O H H H O H O O O 60 27.16667 No Yes o o o o o o O O O O O O O O O O O O O O O O O O O O O O O O O HP POOP PO PO PP OOOP POOP PPP POOPOPPY 132 Male 133 Female 53 27.16667 No Yes 134 Female 25 27.34043 Yes No 135 Female 35 27.625 No No 136 Male 63 28 No Yes 137 Male 28 28 Yes No 138 Female 42 28.33333 Yes No 139 Male 44 28.33333 No No 140 Female 28 28.62 Yes No 141 Male 24 28.775 No No 142 Male 27 28.85 No No 143 Female 26 28.92105 Yes No 144 Female 59 29.08333 No Yes 145 Male 23 29.30909 No No 146 Male 40 29.69767 Yes Yes 147 Male 22 31 Yes No148 Female 50 31.11111 No Yes O 149 Female 65 31.125 Yes No 150 Male 28 31.2093 Yes No 151 Male 30 31.42857 Yes No 152 Female 37 31.66667 No Yes 153 Male 32 32.34375 No No 154 Female 25 32.42105 No No 155 Male 32 32.5 No Yes 156 Female 51 33.18605 No Yes 157 Male 35 33.33333 No Yes 158 Male 27 33.4 Yes Yes 159 Male 38 34.375 No No 160 Female 64 34.87273 No No 161 Male 26 34.92 Yes No 162 Female 34 37.09302 No Yes O O H O O H O O H O O O H O H H O O O H H H H O O H O O O H HOPOOH POOH OH OH HO H OPP HO HO HOP POO 163 Male 27 37.44737 No Yes O O O H O H O O O O O O H O O O H O O H O O O O O O H P P o o o o o o O O O O O O O O O O O O O O O O O o O O O O 0 0 0 164 Male 37 37.5 No No 165 Female 33 37.6 Yes Yes 166 Male 23 38.15789 No No 167 Female 30 38.35 No No 168 Male 37 38.35 No No 169 Female 41 38.46154 No Yes 170 Female 27 38.8 No No 171 Male 26 38.85185 No No 172 Male 35 39 Yes Yes 173 Female 29 39.5 No No 174 Female 55 39.85 Yes No 175 Male 42 39.95 No Yes 176 Female 22 40 No No 177 Male 30 40.04546 No No 178 Female 61 41.66667 Yes No O179 Female 41 41.83636 Yes No 180 Male 29 42.44186 No No 181 Female 59 42.51351 No Yes 182 Male 37 43.02222 No No -OPPPOPO 183 Male 29 43.15 No No 184 Male 46 43.16 Yes No OHOOOH HOOOOP 185 Female 32 43.34286 Yes No 186 Male 50 43.85965 No Yes 187 Male 30 44.6 No Yes 188 Male 33 44.75555 No No 189 Female 33 44.86666 Yes No 190 Male 40 46.02 No No 191 Male 44 46.02 Yes Yes 192 Male 26 46.42105 Yes No 193 Female 58 47.95 Yes Yes OHH PO P P P O O O O O O O HO HO OOH HOOOOHOO o o o o o o o o o o o o o O O O O O O O O O O O O O O O O O 194 Female 31 48.075 No No 195 Female 36 48.2 Yes No 196 Female 46 48.9 Yes No 197 Male 32 49.02222 Yes No 198 Male 55 50.92857 Yes No 199 Male 46 52.94 Yes No 200 Male 37 56.25 Yes No 201 Female 43 56.4 No Yes OPOOPY 202 Male 64 57.525 No Yes 203 Male 36 61.38 Yes Yes 204 Male 36 61.5 No No 205 Male 49 61.72093 No Yes 206 Male 31 68.94736 Yes Yes 207 Female 60 70 No Yes 208 Male 42 70.21277 Yes No 209 Male 35 70.83334 Yes No 10 0210 Male 31 73.1 No Yes 211 Male 38 73.64 Yes Yes 212 Male 38 78.26 Yes No 213 Female 43 79.68571 No Yes 214 Male 38 79.88889 Yes No OOH P P P P PO PPP 215 Male 63 80 Yes No o o o o o OOO OOO OH OO OHHOPPO 216 Male 56 87.5 No Yes 217 Male 64 91.17647 No Yes 218 Male 31 100 No No 219 Male 53 100 Yes Yes P 220 Male 44 100.5814 No No O