y = X,B1 + X,B2 + ɛ where y = (y1, .., Yn)', X1 and X2 are random except the intercept term (i.e., th vector of 1) included in X1. Conditional on Xı and X2, the random error vecte ɛ is jointly normal with zero expectation and variance-covariance matrix V, which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some off-diagonal elements are nonzero). B1 and B2 are vectors of two different sets of regression coefficients; B1 has two regression coefficients and B2 has four regression coefficients. B = (B1 , B½)'; that is, B is a column vector of %3D six regression coefficients. a) V is completely known (i.e., the values of all elements of V are given).

A financial analyst is examinıng the Pela each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be y = -0.147+0.043x. This line, along with a scatter plot of her data, is shown below. Earnings per Current stock price, y (in dollars) share, x (in dollars) 36.55 1.64 14.18 0.57 41.79 1.37 39.16 1.10 2.5+ 57.70 2.71 26.95 0.90 32.65 1.70 41.94 1.17 52.79 2.56 42.72 2.01 16.89 0.76 22.46 0.58 Earnings per share, x (in dollars) 58.88 2.19 30.13 1.48 50.08 1.73 28.92 0.81 Submit Assi Continue D 2021 McGraw-H Education. All Rights Reserved. Terms of Use Privacy e to search 近 Current stock price, y (in dollars)

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be: (01 mark) www.thundershare.net O either 0 or 1.0 or-1.0 O either 0 or 1.0 O either 1.0 or -1.0 zero

Curing times in days (x) and compressive strengths in MPa (V) were recorded for several concrete specimens. The means and standard deviations of the x and y values were * = 5, s, = 2, 5 = 1350, s, = 100. The correlation between curing time and compressive strength was computed to be r = 0.7. Find the equation of the least-squares line to predict compressive strength from curing time.

The correlation between the height and weight of children aged 6 to9 is found to be about r=0.8 . Suppose we use the height x of a child to predict the weight y of the child. We conclude that: a) the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64 . b) the least-squares regression line of y on x would have a slope of 0.8. c) height is generally 80 % of a child’s weight. d) about 80 % of the time, age will accurately predict weight.

A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear regression model displayed was used: profits = a + B (sales), where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least squares. The results displayed were obtained from statistical software. 2 = 0.662 S = 466.2 Parameter Std. err. of Parameter estimate parameter est. -176.644 61.16 0.092498 0.0075 Suppose the researchers test the hypotheses Ho: P = 0, II, : A > 0. The P-value of the test is: less than 0.01. between 0.05 and 0.01. O between 0.10 and 0.05. greater than 0.10. hp

Suppose we are given a least squares regression line ˆy= 4.3x +10. If a data point used to obtain the regression line is (1.5, 16) then the residual at that point is which of the following:  (i) 0.45 (ii) -0.45 (iii) 0.55 (iv) 16.45

A set of paired data has a least squares regressionline with equation yn = 0.50x + 2.0 and a correlationcoefficient of r = 0.80. Suppose we convert the datafor each variable to z-scores and then compute the newregression line. What will the equation be?A) zˆy = 0.50zx B) zˆy = 0.64zxC) zˆy = 0.80zx D) zˆy = 0.50zx + 20E) zˆy = 0.80zx + 20

What happens to the sum of the squared residuals as the data gets closer versus farther from the best fit regression line

29) Two variables are measured on a random sample of n = 23. The sample data results ina sample correlation of 0.393. If you fit a simple regression model to the data, whatvalue would the coefficient of determination (or R-squared) take on?A) 0.627B) 0.393C) 0.154D) 0.000E) 0.296