DO QUALITY WORK OR I WILL REQUEST REFUND!!!

Given a dataset of X and Y values, calculate the least-squares estimates of the slope and intercept for a simple linear regression model, and interpret their meaning in the context of the data.

For a dataset with three independent variables (X1, X2, X3) and a dependent variable (Y), perform multiple linear regression and determine the coefficients of each independent variable. Are all the variables statistically significant?

Conduct residual analysis on a set of residuals from a linear regression model to check for assumptions like normality, homoscedasticity, and independence. Suggest any necessary transformations or model adjustments based on your findings.

Perform a hypothesis test to determine if there is a significant relationship between an independent variable (X) and the dependent variable (Y) in a simple linear regression model. State the null and alternative hypotheses and calculate the test statistic.

Calculate the probability of rolling a pair of fair six-sided dice and obtaining a sum greater than 9. Show your work and provide the probability as a fraction.

In a deck of 52 cards, what is the probability of drawing two consecutive cards (without replacement) that are both spades? Calculate this probability step by step.

Given information about a medical test’s sensitivity, specificity, and the prevalence of a disease, use Bayes’ theorem to calculate the probability that an individual who tests positive actually has the disease.

Consider two random variables X and Y with known probability density functions. Find the probability density function of the sum Z = X + Y. Show the steps in deriving the probability density function for Z.

Requirements: 8PGS