Write/modify the code to calculate the following two empirical probabilities (e.g., all 1599 rows as sample data): a) Probability of red wine quality to be less than 5, i.e., P(X12.48 PMLet us assume...

Write/modify the code to calculate the following two empirical probabilities (e.g., all 1599 rows as sample data): a) Probability of red wine quality to be less than 5, i.e., P(X12.48 PMLet us assume that French wine makers and producers claim that it is possible to produce next year 1,000,000 bottles of red wines, to be considered as a population, a) with an average of quality equal or greater than 7, b) the distribution of quality scores will not be equal. Write the code, which states the Null (Ho) and alternative (H1) hypotheses such that you either reject or accept these two claims, (a) and (b), with confidence values 98% and 95%, respectively, on the basis of evidence provided by your 1599 large sample data12.48 PM. You make now an attempt to improve your linear regression model by turning it into a polynomial expression, i.e., adding as parameters squared variables and/or their combinations. For instance, your model should take the form: y = a +b1X1 + b1X12 + b2X1X2 + ….+error. Write/modify the code such that different degrees up to 5 are tried out. In your attempts, you may opt for suppressing the Intercept. Subsequently, state your observations on how the performance of these models is improved in terms of the R-square metric. Finally, explain whether an improved performance, as measured by the R-square metric, can be trusted and suggest ways to prove this trust12.49 PM