3. [3] Consider a simple linear regression model for (y, X), Yi = Bo + xiß1+6;, %3D where the e;'s are iid N(0, o²). Show that T2 = F, where T = VMSres/Saa and MSR MSres are used to test the hypothesis Ho : B1 = 0 (in simple and multip
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![3. [3] Consider a simple linear regression model for (y, X),
Yi = Bo + xiß1+ €;,
where the e;'s are iid N(0, o²). Show that T2 = F, where
T =
VMSres/Saa
and
MSR
MSres
are used to test the hypothesis Ho : B1 = 0 (in simple and multip](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20558b52-4577-4084-afb1-2e567bebdba0%2Fc4fbee71-8238-4757-9fbd-c33c2d3cf46c%2Fyxtlejf_processed.jpeg&w=3840&q=75)
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- 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 = --+-xWe wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. RBI's HR's Salary (in millions) 108 38 28.050 86 31 27.500 59 25 25.000 119 31 25.000 103 39 24.050 44 15 23.125 49 11 23.000 111 30 22.750 87 31 22.125 90 18 21.857 49 7 21.667 70 21 21.571 108 35 21.500 56 9 21.143 84 38 21.119 80 14 20.802 17 7 20.000 79 24 20.000 91 31 20.000 97 29 20.000 57 13 18.500 44 8 18.000 104 32 18.000 86 27 18.000 100 25 17.454 62 20 17.000 58 20 17.000 100 29 16.083 127 38 16.000 83 29 16.000 59 30 16.000 54…A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation 7 12 9 3 8 10 5 8 10 15 12 7 0 9 13 Sick 4 0 12 2 0 9 3 5 1 0 7 8 3 17 0 A. r = B. r2 = C. Find the equation of the least squares regression line:�^ = + x. D. What does the regression line predict for the number of sick days an employee took if that person took 11 vacation days that year? (Note that this may not be a reliable prediction. Why?) E. Test the hypothesis that there is a linear correlation between the number of vacation days and the number of sick days. Use a level of significance of 0.05. H0: r = 0Ha: r Not Equal to 0 p-Value =
- and test score (y) is V= 67.3+ 1.07x The same data yield r=0.224 and V=75.2. What is the best predicted test 8) Based on the data from six students, the regression equation relating number of hours of preparation (x) Score for a student who spent 2 hours preparing for the test? Use the given data to find the best predicted value of the response variable.Consider the following data for two variables, x and y. \ table[[x, 9, 32, 18, 15, 26], [y, 9, 19, 20, 16, 22]] (a) Develop an estimated regression equation for the data of the form hat(y) = b + b₁x. (Round bo to two decimal 1 0 places and b₁ to three decimal places.) hat 1 (y) = 8.65 +0.427x Comment on the adequacy of this equation for predicting y. (Use α = 0.05.) The high p- value and low coefficient of determination indicate that the equation is inadequate. The high p-value and high coefficient of determination indicate that the equation is adequate. The low p-value and low coefficient of determination indicate that the equation is inadequate. The low p-value and high coefficient of determination indicate that the equation is adequate. hat 2 (y) = 10.54 +2.618x-0.054x Comment on the adequacy of this equation for predicting y. (Use a =0.05.) The high p-value and low coefficient of determination indicate that the equation is inadequate. The high p-value and high coefficient of…The cotton aphid poses a threat to cotton crops in Iraq. The accompanying data on y = infestation rate (aphids/100 leaves) X1 = mean temperature (°C) x, = mean relative humidity appeared in the article “Estimation of the Economic Threshold of Infestation for Cotton Aphid" (Mesopotamia Journal of Agriculture [1982]: 71–75). Use the data to find the estimated regression equation and assess the utility of the multiple regression model y = a + Bjx1 + Bx2 + e y X1 X2 y X1 X2 61 21.0 57.0 77 24.8 48.0 87 28.3 41.5 93 26.0 56.0 98 27.5 58.0 100 27.1 31.0 104 26.8 36.5 118 29.0 41.0 102 28.3 40.0 74 34.0 25.0 63 30.5 34.0 43 28.3 13.0 27 30.8 37.0 19 31.0 19.0 14 33.6 20.0 23 31.8 17.0 30 31.3 21.0 25 33.5 18.5 67 33.0 24.5 40 34.5 16.0 34.3 6.0 21 34.3 26.0 18 33.0 21.0 23 26.5 26.0 42 32.0 28.0 56 27.3 24.5 60 27.8 39.0 59 25.8 29.0 82 25.0 41.0 89 18.5 53.5 77 26.0 51.0 102 19.0 48.0 108 18.0 70.0 97 16.3 79.5 Given: significance level = 0.05 Required: 1. Regression Equation 2. F and…
- The head of the finance department of Supermarket Company in White Exited, New York City prepared the following table. Values are in thousandpesos. 1.) Plot the Scatter Diagram 2.) Solve and plot for the linear regression equation ( y^= a + bx) on the same graph in a. b=nΣ xy-(Σ x)(Σ y)/n(Σ x2)-(Σ x)2 a=Σ y-bΣ x/n Sales y Cost Radio Advertising 76 10 85 12 80 11 55 6 57 9Suppose 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 =An article described an experiment carried out to assess the impact of the variable x₁ = force (gm), x₂ = power (mW), x3 = temperature (°C), and time (msec) on y ball bond shear strength (gm). X4 = = The estimated regression equation is y = -37.48 +0.2117x₁ +0.4983x2 +0.1297x3 +0.2583x4 Interpret b3 and b4. ● What is the expected value of strength (y) from a force of 35 gm, power of 75 mW, temperature of 200 °C, and time of 20 msec ?
- Researchers examined the relationship between two quantitative variables, x and y. we aim to express the relationship between x and y by using the simple linear regression model Yi= B0 + B1Xi+Ei Σx=50, Σy=-20, Σxy=-100, Σx^2=800, Σy^2=120, n=20 d) Suppose we want to test, at the 5% level of significance, the null hypothesis H0:B1=-1 vs the alternative hypthesis Ha: B1>-1. What is the value of observed test statistic associated with this test e)What is the predicted value of y when x is equal to 2 f) what is the 99% confidence interval for E(Y) when x is equal to 4? g) What is the 95% prediction interval for y when x is equal to -2The large national bank charges local companies for using their services. A bank official reported the results of a regression analysi designed to predict the bank's charges (Y), measured in RM per month for services rendered to local companies. One independent variable used to predict service charge to a company is the the company's sales revenue (X), measured in millions of RM. Data for 21 companies who use the bank's services were used to fit the model. The results of the simple linear regression are provided below. Based on results below, a 95% confident interval for B is (15,30). Interpret the interval. * ŷ = -2,700 + 20X Sxy = 65, two – tailed p – value = 0.034 (for testing B We are 95% confident that the sales revenue (X) will increase between RM15 and RM30 million for every RM1 increase in service charge (Y). We are 95% confident that the mean service charge will fall between RM15 and RM30 per month. We are 95% confident that the average service charge (Y) will increase between…(Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y . Suppose that X1 and X2 are uncorrelated. You estimate β1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.
