2. Given the Cartesian coordinates x- 300 mm with standard deviation o, - 0.04 mm, and y = 400 mm with standard deviation ay - 0.05 mm. Assume x and y are uncorrelated. Compute the polar coordinates r and 0 and their variance-covariance matrix
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- 14.) Choose the value of the Correlation Coefficient (r) that best describes the two plots. Ploti Plot II 8. a. I: -0.96, 11: 0.22 b. 1: -0.22, I: 0,78 c. (: -0.22, : 0.99 d. 1: 0.22, (1: -0.78 e. 1: 0.55, 11: 0.21Certain experimental values of and у are given below (0, -1), (2, 5), (5, 12), (7, 20). If the straight line y==a0° =a,+a¸x is fitted to the above data, the best straight line fit is given by A. . y= 2.8987 + 1.1381x B. y= -1.1381 + 2.8966.x O C. y= 1.1381 - 2.8966x O D. y= 1.2321 - 1.1381.rGiven are the data for two variables x and y. Xi. 6 11 15 18 20 Yi 6 8 12 20 30 D. Compute the standardized residuals. Enter negative values as a negative numbers. 1. ? 2. ? 3. ? 4. ? 5. ? All to the 4 decimal places.
- I asked this question before but the direction of extreme was not answered. Thank uSuppose a researcher collects data on the bacterial contamination, measured in colony-forming unit per milliliter, for both upstream and downstream sections of 35 rivers. The data is plotted with upstream bacterial contamination on the horizontal axis and downstream bacterial contamination on the vertical axis. The Scioto River is an outlier in the ?y‑direction. What must be true about this river? The upstream bacterial contamination for this river is much higher or lower than the rest of the rivers in the data set. The downstream bacterial contamination for this river is much higher or lower than other rivers in the data set that have similar upstream bacterial contamination. This river is an influential observation. The downstream bacterial contamination for this river is much higher or much lower than the rest of the rivers in the data set. The absolute value of the residual of this river is large.55. Explain from the data given below whether A and B are independent. positively associated or negatively associated : N=10,000, (A) = 4500, (B) = 6000, (AB) = 3150. () (A) = 150, (a) = 250, (B) = 20o, (aB) = 125. %3D %3D %3D
- Which of the following linear correlation coefficient suggest a perfect negative linear relationship between two variable value?A) r = 0.327 B) r = -0.721 C) r = 0 D) r = 1.6 E) r = -1Consider the bivariate dataset for variable X and variable Y given by the table. Group Y A 1 2 В 2 2 C 8 1 E 1 4 Solve the following questions. a. Find the sum of Y^2: b. Find the Correlation coefficient: c. Estimate the slope of the regression line:Find the mean and standard deviation for each uniform continuous model. (Round mean answers to 1 decimal place and standard deviation answers to 4 decimal places)a. U(2,15) Mean= Standard deviation=b. U(110,190) Mean=Standard Deviation=c. U(3,97)Mean= Standard Deviation=
- The following scatterplot shows the mean annual carbon dioxide (CO,) in parts (CO2) per million (ppm) measured at the top of a mountain and the mean annual air temperature over both land and sea across the globe, in degrees Celsius (C). Complete parts a through h on the right. f) View the accompanying scatterplot of the residuals vs. CO2. Does the scatterplot of the residuals vs. CO, show evidence of the violation of any assumptions behind the regression? 16.800 A. Yes, the outlier condition is violated. 16.725 O B. Yes, the linearity and equal variance assumptions are violated. 16.650 C. Yes, the equal variance assumption is violated. 16.575 O D. No, all assumptioris are okay. 16.500 O E. Yes, all the assumptions are violated. 325.0 337.5 350.0 362.5 CO2 (ppm) OF Yes, the linearity assumption is violated. his vear, What mean temperature doesA fuel company wants to find the functional relation between the amount of gas it sells for heating and the daily temperature. Given the values for 10 observations ∑x= - 50, ∑x^2 = 626, ∑y^2 = 6432 ∑y= 222, ∑xy= —1743 for the daily average temperature and gas sales (in thousand liters). a) Obtain and interpret the correlation coefficient for the variables.b) Set up the regression equation and interpret the coefficients.c) Find R2 and interpret.d) When the temperature is 10 degrees, please observe the gas sales amount.2) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231