Question 1

1. Write down the value of the crime rate per thousand population in Yorkshire and the Humber. Briefly describe and explain the data type in Table 1.
2. Calculate the sample mean and sample standard deviation for both the “Unemployment Rate” and “Crime Rate per Thousand Population” variables.
3. Assume that the crime rate per thousand population acts like a draw from a normal distribution with a mean and standard deviation given in part.
4. What is the probability that the crime rate per thousand population is greater than 100?

Question 2

Use the information in Table 1 to estimate and interpret the intercept and slope coefficients of a bivariate linear regression model of crime rate per thousand population on unemployment rates

Question 3

1. Calculate the residual sum of squares (RSS) and total sum of squares (TSS) from the estimated model in Question 2.
2. Use the RSS and TSS to calculate and interpret the R2 .
3. Perform a hypothesis test where the null hypothesis is that the coefficient associated with the "Unemployment Rate” variable is zero, based on the results you obtained in Question 2.
4. Write the equation of Question 2 in matrix form.