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\fQuestion 4. Least squares solution [6 marks] The ordinary least squares estimate for the slope in simple linear regression gives the following: () qiyi) - ny Show that this is the same as B1= 12(1 -F)(U - V) ELI(r - )2 where 1 = = yi . i-1 i-l1. What does a positive linear relationship between x and y in a simple regression imply? (a) Increases in the independent variable are usually accompanied by increases in the regressor (b) The relationship between x and y cannot be explained by a straight line (c) Decreases in the independent variable is usually accompanied by increases in the regressors (d) Increases in the regressor are usually accompanied by increases in the dependent variable. 2. Which of these is NOT a reason for adding a disturbance term to a regression model Ve = a + Bx, + ut? (a) Some determinants of the dependent variable may be omitted from the model (b) Some determinants of the dependent variable may be unobservable (c) Some determinants of the independent variable may be omitted from the model (d) There may be errors in the way that the dependent variable is measured which cannot be modelled. The condition required to answer questions 3 and 4: Given a regression as ye = a + BX; + ut, suppose you have calculated the following regression results: ), = 1.25 + 0.64x,. The standard errors of & and & are 1.22 and 0.58, respectively. 3. Using the test of significance approach, what is the test statistic value of a hypothesis to test whether the true value of B statistically different from zero? (a) -0.62 (b) 0.91 (c) 1.10 (d) Cannot say without more information.Homework: Chapter 4.2 Least-squares Regression Save Score: 0 of 1 pt 3 of 8 (6 complete) HW Score: 53.93%, 4.31... 4.2.13 Question Help The least-squares regression equation is 55000- y = 595.0x + 18,876 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter Median Income diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7340. 25000- Complete parts (a) through (d) 15 20 25 30 35 40 45 50 55 60 Bachelor's $% (a) Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree (Round to the nearest dollar as needed.)