The polynomial regression model of degree r is given by Y₁ =B₁ + B₁X₁ + B₂X² + ... + ³₂X² + U₁. Interpret the coefficient 3, in a linear regression (r = 1): Y = Bot Bi Xit and in a quadratic regression (r = 2): Y₁ =B₁ + B₁X₁ + B₂X² + U₁. How is the estimation affected if we estimate a linear regression (r = 1) when the true form of the regression function is quadratic (r = 2) or cubic (r = 3)?
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- Does Table 1 represent a linear function? If so, finda linear equation that models the data.A linear regression of age (x) on blood lead levels (y) for men who have worked in factories that manufacture car batteries is performed. The residual plots suggest there is still a pattern remaining, and you decide to add a quadratic term (age2) for age into the model. Which of the following models is now most appropriate? Blood lead levels = a + b21 (age) + e, e ~iid N(0, s2) Blood lead levels = a + b1 (age) + e2, e ~ iid N(0, s2) Blood lead levels = a + b1 (age) + b2 (age2) + e, e ~iid N(0, s2) Blood lead levels = a + b1 (age2) + e, e ~iid N(0, s2)A study tests the effect of earning a Master's degree on the salaries of professionals. Suppose that the salaries of the professionals (S,) are not dependent on any other variables. Let D, be a variable which takes the value 0 if an individual has not earned a Master's degree, and a value 1 if they have earned a Master's degree. What would be the regression model that the researcher wants to test? A. S,= Po + B,D,+u, i=1, .. , n. O B. S,= Po + B, + u, i= 1, .. , n. OC. 1=6o +B1,S, + u, i= 1, .. , n. O D. 0=Bo +B, S, + u,, i= 1, .. , n. Suppose that a random sample of 160 individuals suggests that professionals without a Master's degree earn an average salary of $59,000 per annum, while those with a Master's degree earn an average salary of $80,000 per annum. The OLS estimate of the coefficient B, will be $ and that of B, will be $ Click to select your answer(s). DELL
- 1) create a line in DESMOS with the linear regression equation: y1 ~ mx1 + b 2) create a second line with quadratic regression: y1 ~ ax1^2 + bx + c After looking at the regression in DESMOS, is the data LINEAR or QUADRATIC?What is the equation for a simple linear regression model that predicts the dependent variable Y based on a single independent variable X?29. Below is the result of running linear regression in R. The least-squares regression equation is Call: Lm(formula = variable_C ~ variable_W) Coefficients: (Intercept) -5.5162 variable_W 0.2666 A. variable_W -5.5162 + 0.2666 * variable C B. variable C = -5.5162 + 0.2666 * variable W C. variable W = 0.2666 – 5.5162 * variable C D. variable_C = 0.2666 – 5.5162 * variable_W B. bO. None of the above. MacBook Air DD 80 888 000 F3 F4 F6 F7 F8 F9 F5 # $ & 8
- The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). A multiple linear regression analysis was applied to the experimental data using MINTAB and the following results were obtained: Regression Analysis: y versus x1, x2, x3, x4 Regression Equation y = -123 + 0.757 x1 + 7.52 x2 + 2.48 x3 - 0.481 x4 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -123 157 -0.78 0.459 x1 0.757 0.279 2.71 0.030 2.32 x2 7.52 4.01 1.87 0.103 2.16 x3 2.48 1.81 1.37 0.212 1.34 x4 -0.481 0.555 -0.87 0.415 1.01 Analysis of Variance Source DF Seq SS Seq MS F-Value P-Value Regression 4 5600.5 1400.1 10.08 0.005 Error 7 972.5 138.9 Total 11 6572.9 Then, the upper limit of the two-sided 95% confidence interval on the slope B2 is equal to а. 17 O b. 20 19The equation used to predict annual cauliflower yield (in pounds per acre) is y = 24,121 +4.505x₁ -4.772x₂, where x₁ is the number of acres planted and x2 is the number of acres harvested. Use the multiple regression equation to predict the y-values for the values of the independent variables. (a) x₁ =35,100, x₂ =35,500 (b) x₁ = 36,800, X2=37,100 (c) x₁ = 37,900, x₂ = 38,000 (d) x₁ =41,100, x₂ = 41,200 (a) The predicted yield is pounds per acre. (Round to one decimal place as needed.) (b) The predicted yield is pounds per acre. (Round to one decimal place as needed.) (c) The predicted yield is pounds per acre. (Round to one decimal place as needed.) (d) The predicted yield is pounds per acre (Round to one decimal place as needed.)The estimate of b in the regression equation y=a+bx+error by the method of least square is