1.42 4.11 4.22 12.28 9.16 28.62 7.92 24.82 9.59 29.82 Find estimates for the linear model yi N(0,0²). Bo+Bixi +Ei where ei ~ That is find Bo, B1, 6. Also perform a test of the null hypothesis Ho B₁ = 0 at level a = 0.01. 1
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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.022) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231Heights (om) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 41 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x 167.74 cm, y 81.46 ko, r0.239, Pvalue 0.017, and y - 106 + 1,15x. Find the best predicted value of y (weight) given an adult male who is 153 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 153 cm tall is kg. (Round to two decimal places as needed.)
- 2. Find the normal equations to the curve 2* = ax + bx + c %3D 2 = ax+ bx + cHeights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 194 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x 167.75 cm, y=81.58 kg, r0.318, P.value = 0.001, and y-109 1.14x. Find the best predicted value of y (weight) given an adult male who is 184 cm tal, Use a 0.05 significance level. The best predicted value of y for an adult male who is 184 cm tall is kg. (Round to two decimal places as needed.)Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 192 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x 167.67 cm. y=81.53 kg. r=0.356, P-value=0.000, and y= -106 +1.14x. Find the best predicted value ofy (weight) given an adult male who is 177 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 177 cm tall is kg. (Round to two decimal places as needed.)
- 3. Fit a least squares quadratic curve to the following data and estimate Y at X = 2.4 fig. 03 2 3. 4. గోలిగౌజి రర్ Y 1.7 1.8 2.3 2.3 A. The required least squares quadratic curve(parabola) and the estimated value of Y at X=2.4? * 大 O Y= 2- 0.5X + 0.2X^2; Y = 1.952 Y= 2-0.6X+ 0.2X^2; Y = 1.712 O Y= 2.1 - 0.5X + 0.2X^2;Y = 2.052 Y= 2- 0.5X + 0.4X^2; Y = 3.104A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + eA) A linear regression has a =6 and b=5 what is y predicted as when x=9? B) A linear regression has b=3 and a=4.What is the predicted Y for x=7?
- Suppose that n = 50, i.i.d observations for (Y₁, X₁) yield the following regressions results: Ỹ= 49.2 + 73.9 X, SER = 13.4, R²=0.78 (23.5) (16.4) Another researcher is interested in the same regression, but makes an error when entering the data into a regression program: The research enters each observation twice, ending up with 100 observations (with observation 1 entered twice, observation 2 entered twice and so forth). Using these 100 observations, what results will be produced by the regression program? Complete the spaces in the equation below. Report the intercept and slope to one decimal place, but report the R2 to two decimal places. Ŷ = + * X, R² =6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)4. Find the parameters and equation of the least squares regression line using the points (1,0), (3,3), and (5,6). 1 A = (XTX)-'xTY = where X = 1 3 and Y = 3 5. 11 answer 3 3 y = --+-x