3) Consider a simple linear regression model Y = Bo + B₁x + €, where Y is the response variable,x is the explanatory variable and € is the random error. Suppose we have n observations(x₁, Y₁), ..., (xn, Yn) on x and Y. Write down the assumptions about the random errors€1,..., En.

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Answered: 3) Consider a simple linear regression…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Use the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).
For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)
6. Government initiated a new pension program, in which employees are allowed to determine his/her annual pension contribution ratio. To investigate what factors will affect the decision on contribution ratio, researcher surveyed 185 employees coming from 10 firms and set up the following regression model. contrib, = Bo + Bearns, + B,age, + Bmale + B,mrate, + ue (1) Where, i denotes firm; e denotes employee; contrib, denotes firmi employee e's annual pension contribution ratio; earns denotes the employee's annual income; age denotes the age of employee e;male is a dummy variable, with value of 1 if the employee is male, 0 otherwise; mrate, denotes the pension contribution ratio made by firm i; u denotes the disturbance term. This model is satisfying the six assumptions for classic linear regression model. OLS estimation results are reported as follows (standard errors are reported in the parentheses) : contrib,e = 0. 12 + 0.24earnsie + 1.2ageie - 2.46maleie + 0.66mrate; (0.06) (0.06)…
The annual energy consumption in billions of Btu for both natural gas and coal is shown for a random selection of states. Gas 223 474 377 289 747 146 Coal 478 631 413 356 736 474 If 500 billion Btu of natural gas is used then what is the projected amount of coal that is usedThe projected amount of coal that is used is billion Btu. (Use your regression equation with the rounded values for m and b to find your answer to this question. Round your answer to THREE decimal places, add extra zeros at the end, if needed) (Round answer to 3 decimal places, for example, XXX.XXX)
9) For the same set of observations on a specified dependent variable, two different independent variables were used to develop two separate simple linear regression models. A portion of the results is presented below. R² (R-squared) Model 1 0.92 Based on R2 of each model, which model is more useful? Why? Model 2 0.85
In the two regression lines are 3y + 9x = 46 and 3x + 12y = 19, determine which one of these is the regression line of y and x and which one is that of x and y. Also find the mean, correlation coefficient and ratio of the variance of x and y?
Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient. Please dont use excel
In the simple linear regression model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be a) close to either -1 or +1 b) close to zero c) close to -1 d) close to +1 ( don't hand writing solution)
Can you help me with this question?
The manufacturer of Beanie Baby dolls used quarterly price data for 2012/-2020/V (t = 1, ..., 36) and the regression equation Pt= a + bt+c₁D1 t + c2 D2 + + c3 D3 t to forecast doll prices in the year 2021. Pt is the quarterly price of dolls, and D1, D2t, and D3+ are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE P-VALUE ON F 0.0001 OBSERVATIONS: F-RATIO 76.34 STANDARD 36 0.9078 PARAMETER VARIABLE ESTIMATE ERROR T-RATIOP-VALUE INTERCEPT 24.0 6.20 3.87 0.0005 T 0.8 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.0 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 The estimated quarterly increase in price is and the estimated annual increase in price is Multiple Choice O O $1.50; $6.00 $1.40; $4.00 $0.60; $2.40 $0.80; $3.20 None of the choices are correct.

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3) Consider a simple linear regression model Y = Bo + B₁1x + e, where Y is the response variable, x is the explanatory variable and e is the random error. Suppose we have n observations (x₁, Y₁), ..., (xn, Yn) on x and Y. Write down the assumptions about the random errors €₁,..., En.