Example 10. In a partially destroyed laboratory record of ananalysis of a correlation data, the following resutls only are eligible :Variance of x = 9Regression equations : 8x – 10y + 66 = 0, 40x – 18y = 214What were (a) the mean values of x and y, (b) the standard deviationof y, and (c) the co-efficient of correlation between x and y.

Answered: Image /qna-images/answer/afb7f5f4-a5de-4b77-aa2b-c923d16476ad.jpg

Answered: Example 10. In a partially destroyed…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age Bone Density34 35745 34148 33160 32965 325 Step 3 of 6: Determine the value of the dependent variable yˆ at x=0.
Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.867 and the equation of the regression line is y = 3.57 + 0.97x, where x represents the IQ score of the younger child. Also, the 20 x values have a mean of 96.75 and the 20 y values have a mean of 97.1. What is the best predicted IQ of the older child, given that the younger child has an IQ of 95? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted IQ of the older child is (Round to two decimal places as needed.)
. 26 You are given : Variance of X = 9 The Regression Equations are 8 X - 10 Y + 66 = 0 40 X - 18 Y = 214 Find (1) Average values of X andY (ii) Correlation Coefficient between the two variables (iii) Standard Deviation of Y.
The fish in my pond have mean length 12 inches and mean weight 5 pounds. The correlation coefficient of length and weight is .8. If the length of a particular randomly selected fish is reported to be 12 inches, then what should we predict for the weight of that fish using simple linear regression?
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.) C) Does the regression equation account for a significant portion of the variance in GPA? Use alpha = 0.05 to evaluate the F-ratio. A) b=0.00375; a=0.925; Y (hat) = 0.00375X+0.925 B) r= 0.5 r^2= 0.25
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age Bone Density34 35745 34148 33160 32965 325 Step 5 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Sir Francis Galton, in the late 1800 s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest (adult) son. The data are given in tabular form and also displayed in the scatter plot below, which gives the least-squares regression line as well. The equation for this line is y =95.35 +0.48 x Height of Height of son, father, x (in centimeters) centimeters) y (in 175.8 178.1 193.5 190.3 210. 183.2 176.6 173.3 171.1 200- 183.8 186.5 190. 175.8 175.6 180 159.8 167.2 xx 170 155.5 175.8 162.0 172.1 160- 190.9 188.0 150 180.1 187.1 Tdo ito Ido 130 200 z1o 186.9 177.5 171.5 181.5 Height of father, x (in centimeters) 190.5 195.7 201.0…
The data is given as follow. xi 2 6 9 13 20 yi 7 18 9 26 23 The estimated regression equation for these data is = 7.6 + .9x.Compute SSE, SST, and SSR (to 1 decimal). SSE SST SSR What percentage of the total sum of squares can be accounted for by the estimated regression equation (to 1 decimal)? %What is the value of the sample correlation coefficient (to 3 decimals)?
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 39 43 46 61 64 Bone Density 352 346 321 314 312 Table Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + bjx, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1 1.5 2.5 4 4.5 Overall Grades 97 93 85 74 72 71 66 Table Copy Data Step 4 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable…
r. What property of 2. If byx = -3/2, bxy = -3/2, find the correlation coefficient, regression coefficient shall apply? %3D
Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.

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