Q 1. interest y. Consider the following bivariate data of an independent variable x and dependent variable of X y 1 1 2 3 4 6 0 0 3 2 1 0 0 -1 -2 -15 (a) Calculate the mean, sample variance and sample standard deviations for x and y. Hint: Recall the formula for sample variance of x 8²=1-1 (₁-2)²2 (Σ1 ) – }(Σ.)2 n-1 n-1 = (b) State the Chebyshev's and empirical rule for the proportion of samples that approximately lie within two standard deviations of the mean for the variable y. Clearly state the intervals and any assumptions. (c) The sample correlation coefficient is given by Σ(₁-7)(y- ÿ) νΣ. (π. - 7) Σ" 1(: - g)2 Calculate r and comment on the relationship between x and y.

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately ?2 = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s2 = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1.   Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)   What are the degrees of freedom?

If y is the dependent variable and is the independent variable. And if the sum of the cross product of the deviations is (x − x)(y – y)= -54, and also if 10.20 and 5.91 are the variances for the independent and dependent variables, respectively, and we have a sample size of 16, what is the correlation coefficient between X and y? Note: 1- Round your intermediate numbers to 4 decimal places. 2- Round your final answer to 2 decimal places. Your Answer:

Compute mean, variance, and standard deviation

12. The components of the OLS variances Under assumptions MLR.1 through MLR.5, conditional on the sample values of the independent variables, the variance of B; under OLS is: Var (B) sST, (1-15) where o2 = the variance of the error term SST; = the total sample variation of a; R; = the R-squared from a regression of r; on all of the other explanatory variables, along with an intercept parameter The variance of Bi v as R; increases. decreases For the given mode e following would lead to a reduction of the sampling variance of B;? increases O Adding variable that is equal to 5+ *j O Using the same data set with the same number of observations O Adding irrelevant explanatory variables to the model that are correlated with r; O Choosing an explanatory variable z that is uncorrelated with the other explanatory variables in the model