Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression" originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: Studenth=19.6+ 0.73x Midparh, R²=0.45, SER=2.0 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.) For the following questions except (d), type your answers in two decimal places. (a) If we test for the statistical significance of the slope coefficient, the relevant f-statistic is f = (b) Construct a 95% confidence interval for a one inch increase in the average of parental height: ( (c) The prediction for the height of a child whose parents have an average height of 70.06 inches is (d) The model explains percent of the variation in the height of students. Hint: type an integer. inches.

A researcher investigating whether government expenditure crowds out investment estimates a regression on data for 30 countries. I-investment; G-government recurrent expenditure; Y=gross domestic product; all measured in $US billion. P= population measured in million. Standard errors are in parentheses. Î= 18.10 (7.79) R² = 0.99 1.07G + 36Y (0.14) (0.02) She suspects that countries with higher GDP may have more variability in their investment. She sorts the observations by increasing size of gdp per capita (Y)and estimates the regression again for the 11 countries with the lowest gdp(Y)and the 11 countries with the largest gdp(Y). The RSS1 from the first regression is 7186. The RSS2 from the second regresison is 28101. Perform a Goldfeld-Quandt Test at a 5% significance level. a. The test statistic for this test is 0.256 b. The critical value defining the rejection region for Ho is 3.18 c. Is there heterscedasticity? Yes=1 or No-0. The answer is 0

We have a random sample of workers from a large firm. In 2017, the firm ran a training program. Some workers did the training program, others did not. The firm now wants to assess the effect of the training on earnings.  We use the following model to estimate the effect of a training program on annual earnings in 2018: ln⁡(earn2018)=β0+β1train+β2ln⁡(earn2016)+β3educ+β4exper+u where earn2018 = individual total annual earnings in 2018 in dollars train = a dummy variable that takes the value 1 if the individual worker did the training in 2017 and 0 otherwise earn2016 = individual total annual earnings in 2016 in dollars educ = the individual's years of education    exper = the individual's years of experience   We find: ln⁡(earn2018)^= 11.672 + 0.041train + 0.821ln⁡(earn2016) + 0.037educ + 0.012exper                          (5.864)   (0.019)         (0.258)                       (0.013)         (0.007) n=1278, R2= 0.048 Which of the following is the correct interpretation of the…

What is meant by the assumption that the paired sample observations ofYi and Xi are independently and identically distributed? Why is this animportant assumption for ordinary least-squares estimation? When is thisassumption likely to be violated?

The management of a large firm would like to know something about employee morale and the other variables to which it may be related. To study these relationships, each employee in a simple random sample of 27 employees is interviewed and tested to obtain information concerning morale level and the average number of satisfying extra work social contacts experienced during a week. Whether or not the duties the employee usually performs are appropriate to the job title is also determined. The dependent variable Y is measure of morale, the quantitative independent variable, X1 is average number of social contacts, and the following dummy variable coding is used to quantify the qualitative variable: X₂ = 1 if yes, X₂ = 0 if no. The model including dummy variable and the interaction term was being estimated and a part of computer outputs is below:

In regression model: Yi = B1+ B2Xi+ Ei, where Ei is a random variable independent of Xi, with mean and variance constant and different from zero. Ei ~(media, varianza) Obtain the OLS estimator of ẞ2. Show that the properties of finite samples hold.