Q2: For the raw data shown in Table below: 1) Find out which of the x₁ or x₂ variables is better correlated to y. 2) Find out the linear regression lines: y₁ = f(x₁) and y2 = f(x₂) depending on the results of 1) above. X1 1 3 4 6 9 11 14 X2 1 2 3 9 12 15 y 1 2 4 7 8 9 10 5 4 87 5
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.For these (x,y) pairs of data points: 1,5 3,7 4,6 5,8 7,9 Compute . Compute . What is the equation of the regression line?
- A set of n = 4 pairs of X and Y values has a Pearson correlation of r = 0.60 and SSY = 200. The standard error of estimate for the regression equation is _______. a. 8 points b. 10 points c. 6 points d. 4 pointsWhich of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSyA forecaster used the regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 and D3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.80 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.00 3.33 0.0015 D2 25.0 7.20 3.47 0.0010 D3 40.0 15.80 2.53 0.0140 What is the estimated intercept of the trend line in the second quarter?
- A forecaster used the regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 andD3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.80 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.00 3.33 0.0015 D2 25.0 7.20 3.47 0.0010 D3 40.0 15.80 2.53 0.0140 Using the estimation results given above, the predicted level of sales in 2022II is _______ units.Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 9 19 7 26 21 Develop the estimated regression equation for these data. ŷ = (c) Use the estimated regression equation to predict the value of y when x = 6.Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 5 9 14 Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal). y^= + x Use the estimated regression equation to predict the value of y when x = 5 (to 1 decimal).y^ =
- Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual starting salary of an employee with a doctorate degree? (Someone with no work experience). $ What is the predicted bi-annual starting salary of an employee with a bachelor’s degree? (Someone with no work experience). $The slope of a regression line (y on x) is -0.24, we know that SDy=3.2 and SDx=4.0, then the correlation coefficient between the two variables is:A. 0.3B. -0.3C. 0.8D. -0.8