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A bioloigst is willing to udnerstand the relation between weights and ages of chickens following different diets in a farm. To this end, he collects data of 578 observations with the following columns: - Weight (kg) - Time (days) - Diet (categorical) a. Build a simple linear regression consisting of weight as a dependent variable and time as independent variable. Please provide regression coefficients. b. To understand the effect of diet on weight gaint, the biologist also adds diet column to the regression model. Which coefficients are found to be significiant? Answer to this question using marginal hypothesis tests. c. Which model (simple linear or multip linear regression) explains weights of chickens better? Compare the two model using adjusted R2 value. d. Build a polynomial regression model by adding the square of time to the model. e. Provide prediction interval for a chicken which is 9 days old and following the second diet