ore analysis reserve 1) The table below shows the assay results for four samples from a gold-silverdeposit. Determine the least squares regression line equation and use it to estimatethe value of Au for Ag = 12 ppm.Ag (ppm)379Au (ppm)20231511

The least square regression line equation is given by y = a + bx Where a and b are the intercept and…

Answered: 1) The table below shows the assay…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Consider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2
A least squares regression line for the following information: n=30 Ex = 501.6 "Ea = 8724.74 Ey 1338.8 Ey = 61980.14 Ery = 23246.55 %3D 11 << 22 is ŷ = 2.550x + 1.993. %3D Compute the SSE using the formula SSE = SSYY - B, SSXY· -1335.8 O101.6 36.3 42.8 O 19.12
11/15 find the least squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. Round to three decimal places as needed.
(a) The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by the ? which for these data is (b) The value r is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, the value 2 of r is . (Round your answer to at least 2 decimal places.) (c) The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the ? v, which for these data is ?
Bivariate data obtained for the paired variablesx and y are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y =-4.87+1.06x . In the "Calculations" tabl : calculations involving the observed y values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 團 160+ 6-7 G-7) G- х 150+ 111.4 115.6 318.9796 409.9005 5.6930 140 122.2 121.5 143.0416 77.4048 9.9982 132.0 139.8 40.1956 2.5281 22.5625 130+ 138.6 130.1 11.2896 73.7194 142.7069 120- 151.1 160.3 720.3856 476.8109 25.0400 110- Column 1233.8920 1040.3637 206.0007 sums 110 120 130 140 150 160 Send data to Excel Figure 1 Answer the following: 1. The variation in the sample y values that is not explained by the estimated linear relationship between x and y is given by the ? v, which for these data is ? 2. The value r is the…
Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = 14.87+0.88x. In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 160+ x y (x-1)² (-5)² (v-^^)² 150+ 107.2 110.7 396.0100 457.7032 2.2320 122.0 130.3 140- 0.0900 70.0569 65.1249 131.5 122.1 130- 72.2500 0.0001 72.0801 142.5 129.9 120. 0.4900 93.5089 107.5369 152.5 160.0 110- 864.3600 341.1409 119.4649 Send data to Excel LL 130 130 140 150 160 Column sum: 1333.2000 Column sum: 962.4100 Column sum: 366.4388 Figure 1 Answer the following. (a) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an…
For a sample of 15 trees, the volume of lumber (y) (in cubic meters) and the diameter (x) (in centimeters) at a fixed height above ground level was measured. The following summary statistics were obtained: x̄ = 35.2 sx = 8.9 ȳ = 0.78 sy = 0.48 r = 0.95 a) Compute the least-squares regression line for predicting volume from diameter. B)Predict the volume for a tree whose diameter is 42 centimeters
One is interested in the ceteris paribus relationship between the dependent variable y, and the explanatory variable ₁1. For this, one collects data on two control variables Xi2 and Xiz and runs two LS regressions. Regression 1: yi = B₁x₁1 + Ui Regression 2: y = B₁xil+ B₂x₁2 + B3x13 + Ei Let ₁ denote the LS estimate of ₁ of Regression 1 and let ₁ denote the LS estimate of ₁ in Regression 2. Assume that the true model is given by Regression 2 and that all variables are centered. a) Would you expect a difference between ₁ and ₁ when is highly correlated with 2 and 3 and the partial effects of xi2 and xi3 on yi are also high? b) Would you expect a difference between ₁ and 3₁ when ₁ has almost no correlation with and Xi3 but X2 and 3 are highly correlated? Xi2 c) Which of the two estimators is more efficient if x₁1 is highly correlated with 2 and 13, and Xiz have small partial effects on yi? but i2 d) Which of the two estimators is more efficient if x₁1 is almost uncorrelated with 2 and…
Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?
Assume a least squares regression line ŷ = 1.6 + 4.5x, with a standard error for the slope of 0.58 calculated from a sample of 35 observations. (a) Which of the following calculates the test statistic for a hypothesis for slope? t = b − x0 s t = b − 0 sb t = x0 − x s/ n t = b − a sb (b) Calculate the test statistic for the hypothesis test for slope. (Round your answer to two decimal places.)
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. A scatterplot (not shown) revealed the height, in cm and foot length in cm, for each high school student from the sample. The association was described to be strong, positive, and linear. a. In the context of the study, explain what is meant by the following terms: positive: linear: b. The least squares regression equation was predicted height=105.08+2.599 (foot length). One of the students had a foot length of 20 cm. His residual was calculated to be 2.94 cm. What was the height of the student? c. suppose that the distribution of residuals is approximately normal with a standard deviation of 5.9 cm. What percent of residuals are less than 7 cm? Justify why.
A statistical program is recommended.A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:y = 0 + 1x + wherey traffic flow in vehicles per hourx = vehicle speed in miles per hour.The following data were collected during rush hour for six highways leading out of the city.Traffic Flow(y)Vehicle Speed(x )1,247351,320401,218301, 327451,341501, 11325(a) Develop an estimated regression equation for the data. (Round bo to one decimal place and b1 to two decimal places.) =

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1) The table below shows the assay results for four samples from a gold-silver deposit. Determine the least squares regression line equation and use it to estimate the value of Au for Ag 12 ppm. %3D Ag (ppm) 7 9. 11