Part II The built-in "m Eiyltl R contains four variables from different regions of Switzerland called [1&1]than 1888: Fertility lg, 'oommon standardized fertility measure' Agriculture % of males involved in agriculture as occupation Examination % draftees receiving highest mark on army examination Education 96 education beyond primary school for draftees. Catholic % 'catholic' (as opposed to 'protestant'). |nfant.Mortality live births who live less than 1 year. 0 21 15 25 80 40 Agriculture 1 40 25 Examination 30 Education Catholic 60 0 25 15 Share PDF for viewing 40 60 BO 5 15 25 3 40 80 1. On the basis of this scatter plot: a. What kind of relationship (positive, negative or no correlation) do Agriculture, Examination, Education, Catholic and Infant Mortality have with Fertility? b. For each of the variables in part a., estimate the correlation coefficient, r, with Fertility. c. Provide an explanation for why the variable Catholic looks the way it does (is with very few observations in the middle).Below is the output from a regression model in which Fertility is predicted by Agriculture, Education, Catholic and an interaction term between Catholic and Education [l[Catholic'*m,l= Call: lm{Formula = Fertility ~ Catholic r Agriculture 4 Education + ICCathelic * Education), data = swiss) Residuals: Min 10 Median SQ Max 11.396 6.293 1.925 5.?69 14.888 Coefficients: Estimate Std. Error t value PrCsltlj (Intercept) 2.864284 5.223422 .864 a 2e16 Catholic '.295?48 9.951434 '.999 9.999251 Agriculture ..19359? 9.9?95?5 .?43 9.993999 Education 3.?52259 9.269??3 3.?88 9.992923 :\" ICCGtholic * Education) .99?9?6 9.995525 '.444 9.156261 Signi'F. codes: 9 '***' 9.991 '**' 9.91\"\" 9.95 '." 9.1 " " 1 Residual standard error: '2 on 42 degrees of Freedom Multiple Rsquared: . Adjusted Rsquared: 9.626? Fstatistic: 29.31 on 4 and 42 DF, p-value: 2.264e99 a. Write out the equation for the regression estimated above using the regression output. b. Predict Fertility in a Swiss region / Canton with 50% of males in Agriculture, 10% have education beyond primary school and 10% are Catholic. c. Please explain what the adjusted R-squared of 0.6267 means in this context. What does it say about the relationship between Fertility, Agriculture, Education and Catholic? d. What does this regression suggest about factors predicting fertility in Swiss cantons in 1888? Please use p-values and estimates of regression coefficients in your explanation