A group of scientists conducted an experiment to compare the performance of two types of soil on the quality of tomatoes. The goal of the study is to assess if the type of soil affects the "yield" of tomatoes. The yield of a tomato is calculated using its weight and diameter. The units of the yield are leg/ma. A total of 1187 observations were collected. Among these observations. 478 observations were obtained from the standard soil while 709 observations from the new soil. An observation in the data set consists of the yield of a tomato and type of soil used to obtain it. To tackle this problem, the scientists use a simple linear regression model and the statistical software R. Using this software. the scientists produce the output below. 0.4 0.3 0.2 0.1 0.0 Sumdard New Typo.oi'.SoI > contrasts(soil . data$Type . of . Soil) New Standard 0 New 1 > Im. soild summary(1m. soild) Call: Im(formula = Yield ~ Type. of. Soil, data = soil . data) Residuals: Min 10 Median 3Q Max -0. 207175 -0.057175 0. 007209 0.057209 0.212825 Coefficients : Estimate Std. Error t value Pr(>Itl) (Intercept) 0. 192791 0. 003588 53.728 confint(1m. soild) 2.5 % 97 .5 % (Intercept) 0. 18575073 0. 19983086 Type. of . SoilNew 0. 01527493 0.03349327 > anova(lm. soild) Analysis of Variance Table Response: Yield Df Sum Sq Mean Sq F value Pr ( > F) Type. of . Soil 1 0. 1698 0. 169761 27.583 1.783e-07 *** Residuals 1185 7. 2932 0.006155 Signif. codes: 0 '***) 0. 001 '* * ' 0. 01 ' *' 0. 05 '. ' 0.1 ' ''1Residuals vs Fitted Normal Q-Q 2486830 0.2 N 0.1 Residuals 0.0 Standardized residuals O -0.1 N -0.2 0139 092 0.195 0.200 0.205 0.210 0.215 Fitted values Theoretical Quantiles Scale-Location Residuals vs Leverage 1.0 ViStandardized residuals Standardized residuals 0 -1 05 - - . Cook's distance 0.195 0.200 0.205 0.210 0.215 0.0000 0.0005 0.0010 0.0015 0.0020 Fitted values Leverage Using this R output, answer questions Q3.1 to Q3.6. Q3.1 5 Points The reference category used by R is the new type of soil. O True O False Q3.2 5 Points What is the interpretation of the estimated intercept? Use one sentence. In your answer, you can write symbols and equations by putting LaTex or R Markdown expressions between two dollar signs. For example, $$x12$$. Enter your answer hereQ3.4 5 Points Is the constant variance assumption of the residuals satisfied? In up to three sentences, explain why or why not and mention the plot you use to justify your answer. Enter your answer here Q3.5 5 Points Do the residuals follow a normal distribution? In up to three sentences, explain why or why not and mention the plot you use to justify your answer. Enter your answer here Q3.6 10 Points Based on the whole R output and analysis above only, is there evidence to conclude that the new type of soil gives a better yield than the standard soil? In detail, explain why or why not. There is no sentence limit here. Enter your answer here