3. This is data from R. Weintraub (1962), The Birth Rate and Economic Development: An Empirical Study, Econometrica, Vol. 40, #4, pp 812-817. The data set contains birth rates, per capita income, proportion of population in farming, and infant mortality during early 1950s for 29 nations:

Nation................ Birthrate............. Income........ Farm........... IMR

Mexico................. 45.7.................. 118 ..............0.61............ 87.8

Ecuador.............. 45.3 ...................44................... 0.53............ 115.8

Colombia................ 38.6 .................158................ 0.53........... 106.8

Ceylon ...................37.2.................. 81.................... 0.53........... 71.6

PuertoRico............. 35 .....................374.................. 0.37............ 60.2

Chile........................ 34................... 187................... 0.3............. 118.7

Canada................... 28.3................. 993 ....................0.19 ............33.7

UnitedStates............. 24.7 ...............1723................... 0.12 .............27.2

Argentina................... 24.7............... 287.................... 0.2................. 62

New Zealand............... 24.4............... 970................... 0.19.............. 24.9

Australia....................... 22.7............... 885.................. 0.12............... 22.9

Hungary....................... 22.3................ 200................. 0.53............... 65.7

Netherlands................. 21.7 ................575 ....................0.14 .............21.6

Finland.......................... 21.6................. 688.................. 0.34 ..............32.4

Phillipines........................ 21.3............... 48 ......................0.69........... 108.7

Ireland ............................21.2.................. 572................... 0.49 ............38.6

Japan ................................20.8................ 239 ....................0.42............ 46.7

Spain................................ 20.3 ..................244................. 0.48 .............56.5

France ...............................18.9................... 472 ................0.25 ...............44.4

Greece ...............................18.8 ....................134................ 0.52 .............47.4

Norway ...............................18.6 .....................633................... 0.19 ...........21.7

Italy ......................................18..................... 295 .....................0.44 ...........55.7

Denmark ..............................17.6.................... 906 ....................0.24............ 27.1

Switzerland ...........................17...................... 1045 .................0.16.............. 28.5

Belgium .................................16.7..................... 775...................... 0.1 ............41.6

WestGermany ....................15.9 .....................619.................... 0.15 ..............44.6

England .................................15.3 ......................901.................. 0.05 .........26.1

Sweden.................................. 15 .........................910 ................0.24 ..........18.7

Austria ..................................14.8.......................... 556................. 0.22....... 49.1

(a) Choose the best subset of predictors (Birthrate, Income, Farming and IMR) using the forward selection algorithm. To fit the model select Stat Regression Regression Fit Regression Model. Select Birthrate for the response, and select the predictors for each model in the Continuous predictors field. For each step of the algorithm, state which predictors are in the model you are fitting, and include the model summary for each model fit in that step. For example, the first model fit in the first step of the algorithm would be: Income: After completing the algorithm, create a table listing which model you chose for each step and the R2 adj for that model. Based on this table, explain which subset of predictors you should choose based on the forward selection algorithm.

(b) Repeat part (a) using the backwards selection (elimination) algorithm