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2.11.1 Problems 2.1 Consider the following five observations. You are to do all the parts of this exercise using only a calculator. X 3 2 1 -1 y 4 2 3 1 0 0 Σx = | Σy = | Σ(x − 1) = ہ لیا Σ(x-7)(y₁ - y) = a. Complete the entries in the table. Put the sums in the last row. What are the sample means x and y? b. Calculate b, and by using (2.7) and (2.8) and state their interpretation. c. Compute Σ Σ *y. Using these numerical values, show that Σ(x – F) = 2x – Nx and Σ(x-7)(y-7)= Σxy-№xy. =1 d. Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. X₁ 3 x-x 2 1 Calculate the sample variance of y. s= (-3)/(N-1), the sample variance of x, $=(x₁ - x)²/(N-1), the sample covariance between x and y, s,,= (N-1), the sample correlation between x and y, r, s,/(s,s,) and the coefficient of variation of x, CV, = 100(s/x). What is the median, 50th percentile, of x? (₁-3)(x₁ - x)/ = -1 0 Σ(x₁ - x)² = Y₁ 4 2 3 y-y ŷ₁ ê Σ(ν. – 5) = (x-x)(y-y) ê xe 1 0 MW Σy = Σ=Σ = Σ = Σx = e. On graph paper, plot the data points and sketch the fitted regression line ŷ, b₁ + b₂x₁. f. On the sketch in part (e), locate the point of the means (x,y). Does your fitted line pass through that point? If not, go back to the drawing board, literally. g. Show that for these numerical values y = b₁ + b₂. h. Show that for these numerical values y = y, where y = Ey/N. i. Compute ở. j. Compute var (b₂lx) and se(b₂). 2.2 A household has weekly income of $2000. The mean weekly expenditure for households with this income is E(ylx = $2000)=Hy-$2000 = $220, and expenditures exhibit variance var(ylx = $2,000) = $2,000 = $121. yr llu distributed find the probability that a house

2.11.1 Problems 2.1 Consider the following five observations. You are to do all the parts of this exercise using only a calculator. X 3 2 1 -1 y 4 2 3 1 0 0 Σx = | Σy = | Σ(x − 1) = ہ لیا Σ(x-7)(y₁ - y) = a. Complete the entries in the table. Put the sums in the last row. What are the sample means x and y? b. Calculate b, and by using (2.7) and (2.8) and state their interpretation. c. Compute Σ Σ *y. Using these numerical values, show that Σ(x – F) = 2x – Nx and Σ(x-7)(y-7)= Σxy-№xy. =1 d. Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. X₁ 3 x-x 2 1 Calculate the sample variance of y. s= (-3)/(N-1), the sample variance of x, $=(x₁ - x)²/(N-1), the sample covariance between x and y, s,,= (N-1), the sample correlation between x and y, r, s,/(s,s,) and the coefficient of variation of x, CV, = 100(s/x). What is the median, 50th percentile, of x? (₁-3)(x₁ - x)/ = -1 0 Σ(x₁ - x)² = Y₁ 4 2 3 y-y ŷ₁ ê Σ(ν. – 5) = (x-x)(y-y) ê xe 1 0 MW Σy = Σ=Σ = Σ = Σx = e. On graph paper, plot the data points and sketch the fitted regression line ŷ, b₁ + b₂x₁. f. On the sketch in part (e), locate the point of the means (x,y). Does your fitted line pass through that point? If not, go back to the drawing board, literally. g. Show that for these numerical values y = b₁ + b₂. h. Show that for these numerical values y = y, where y = Ey/N. i. Compute ở. j. Compute var (b₂lx) and se(b₂). 2.2 A household has weekly income of $2000. The mean weekly expenditure for households with this income is E(ylx = $2000)=Hy-$2000 = $220, and expenditures exhibit variance var(ylx = $2,000) = $2,000 = $121. yr llu distributed find the probability that a house

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Please solve 2.1 in its entirety, thanks!
are car- y independent of the jth pair to collect data pairs (y,x) ationship between x, and e;. dent of e, if i j. Then, the is, and the implications are independent, ata pairs are re uncorrelated. e assumptions? They are de; (Section 2.10.1) and es estimators are the best on x they have a normal rs, (y₁x₁), i = 1, ..., N, ent and identically dis- data are iid. This is a pulation. showed how the strict is correlation between eity fails with random elated with a value x¡ ndom Sampling = 1,..., N, where m. airs and have the ibuted. uction process by costs. The error m's managers. It action process, so m's input usage is error, e. A firm's endogenous. 2.11.1 Problems 2.1 Consider the following five observations. You are to do all the parts of this exercise using only at calculator. x 3 2 1 -1 0 Σx = y 4 2 3 1 Σ» = | Σ(x − x) = x-x Xi 3 2 1 -1 (x-x)² a. Complete the entries in the table. Put the sums in the last row. What are the sample means x and y? b. Calculate b, and by using (2.7) and (2.8) and state their interpretation. c. Compute Σy. Using these numerical values, show that Σ(x₁ - x)² = x² - Nx² and Σ(x − x)(y – 5) = Σxy – Nxy. d. Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Calculate the sample variance of y, s= E(-y)/(N-1), the sample variance of x, s²=Σ(x₁ - x)²/(N-1), the sample covariance between x and y, sy = (₁-3)(x-x)/ (N-1), the sample correlation between x and y, r = sxy/(s,s,) and the coefficient of variation of x, CV, = 100(s,/). What is the median, 50th percentile, of x? y-y 2(x − x) = | Σ( − 5) = | Σ(x − x)(y - 5) = ŷ₁ Y₁ 4 2 3 1 0 0 Σx = | Σy = | Σ= | Σê=Σ = Σx = ê₁ lalu fand ornan (x-x)(y-y) that point? If not, go back to the drawing board, literally. g. Show that for these numerical values y=b₁ + b₂. h. Show that for these numerical values ŷ = y, where ŷ = Σŷ/N. i. Compute 6². j. Compute var (b₂lx) and se (b₂). xiê; e. On graph paper, plot the data points and sketch the fitted regression line ŷ, = b₁ + b₂x₁. ana.s f. On the sketch in part (e), locate the point of the means (x,y). Does your fitted line pass through 2.2 A household has weekly income of $2000. The mean weekly expenditure for households with this income is E(ylx = $2000) =Hy-$2000 = $220, and expenditures exhibit variance var(ylx = $2,000) = yix-$2,000 = $121. o² mally distributed find the probability that a house-
Transcribed Image Text:are car- y independent of the jth pair to collect data pairs (y,x) ationship between x, and e;. dent of e, if i j. Then, the is, and the implications are independent, ata pairs are re uncorrelated. e assumptions? They are de; (Section 2.10.1) and es estimators are the best on x they have a normal rs, (y₁x₁), i = 1, ..., N, ent and identically dis- data are iid. This is a pulation. showed how the strict is correlation between eity fails with random elated with a value x¡ ndom Sampling = 1,..., N, where m. airs and have the ibuted. uction process by costs. The error m's managers. It action process, so m's input usage is error, e. A firm's endogenous. 2.11.1 Problems 2.1 Consider the following five observations. You are to do all the parts of this exercise using only at calculator. x 3 2 1 -1 0 Σx = y 4 2 3 1 Σ» = | Σ(x − x) = x-x Xi 3 2 1 -1 (x-x)² a. Complete the entries in the table. Put the sums in the last row. What are the sample means x and y? b. Calculate b, and by using (2.7) and (2.8) and state their interpretation. c. Compute Σy. Using these numerical values, show that Σ(x₁ - x)² = x² - Nx² and Σ(x − x)(y – 5) = Σxy – Nxy. d. Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Calculate the sample variance of y, s= E(-y)/(N-1), the sample variance of x, s²=Σ(x₁ - x)²/(N-1), the sample covariance between x and y, sy = (₁-3)(x-x)/ (N-1), the sample correlation between x and y, r = sxy/(s,s,) and the coefficient of variation of x, CV, = 100(s,/). What is the median, 50th percentile, of x? y-y 2(x − x) = | Σ( − 5) = | Σ(x − x)(y - 5) = ŷ₁ Y₁ 4 2 3 1 0 0 Σx = | Σy = | Σ= | Σê=Σ = Σx = ê₁ lalu fand ornan (x-x)(y-y) that point? If not, go back to the drawing board, literally. g. Show that for these numerical values y=b₁ + b₂. h. Show that for these numerical values ŷ = y, where ŷ = Σŷ/N. i. Compute 6². j. Compute var (b₂lx) and se (b₂). xiê; e. On graph paper, plot the data points and sketch the fitted regression line ŷ, = b₁ + b₂x₁. ana.s f. On the sketch in part (e), locate the point of the means (x,y). Does your fitted line pass through 2.2 A household has weekly income of $2000. The mean weekly expenditure for households with this income is E(ylx = $2000) =Hy-$2000 = $220, and expenditures exhibit variance var(ylx = $2,000) = yix-$2,000 = $121. o² mally distributed find the probability that a house-
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