**Relating the Sample Correlation Coefficient and the Parameters**Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment of intensity is constant. That is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it is violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity.The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities \( x \) (in decibels), the Weber fraction \( y \) (in decibels) is shown. Figure 1 is a scatter plot of the data.| Stimulus Intensity, \( x \) (in decibels) | Weber Fraction, \( y \) (in decibels) ||------------------------------------------|--------------------------------------|| 35 | -0.57 || 40 | -0.1 || 45 | -1.46 || 50 | -1.02 || 55 | -1.96 || 60 | -2.62 || 65 | -3.15 || 70 | -3.16 || 75 | -4.23 || 80 | -4.24 |**Figure 1: Scatter Plot Description**The scatter plot on the right shows the data points plotted with stimulus intensity (in decibels) on the x-axis and Weber fraction (in decibels) on the y-axis. The data points suggest a downward trend, indicating a potential negative correlation between the stimulus intensity and the Weber fraction.The least-squares regression line for these data has a slope of approximately \(-0.0039\).**Questions:**(a) What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least four decimal places.(b) What is the value of the sample correlation coefficient for these data?

X Y X.Y X2 Y2 35 -0.57 -19.95 1225 0.3249 40 -0.1 -4 1600 0.01 45 -1.46 -65.7 2025 2.1316 50…

Answered: Weber's law, a concept taught in most…

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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For the following questions, THERE IS NO NEED FOR EXPLANATION. PLEASE PROVIDE JUST THE ANSWER THANK YOU. Please DO NOT waste time on writing things to explain. Please answer in 30 mintues or else I will write a bad review. If you follow my rules and answer in less than 30 mintues then I will write a very long and wonderful review about you. ANSWER the questions correlty and please answer all the questions with what it regards in saying exactly.
Age, x 16 25 39 45 49 64 70 29 57 22 Systolic blood pressure 109 122 143 132 199 185 199 130 175 118 4. If x is 30 , what would you expect y (in mm ??) to be?
The braking distance required for a car to stop depends on numerous variables such as the speed of the car, the weight of the car, reaction time of the driver, and the coefficient of friction between the tires and the road. For a certain vehicle on one stretch of highway, the braking distances d(s) (in ft) are given for several different speeds s (in mph). 30 35 40 45 50 d(s) 109 134 162 191 223 55 60 65 70 75 256 291 328 368 409 (s)P a. Use regression to find a quadratic function to model the data. b. Use the model from part (a) to predict the stopping distance for the car if it is traveling 62 mph before the brakes are applied. Round to the nearest foot. c. Suppose that the car is traveling 53 mph before the brakes are applied. If a deer is standing in the road at a distance of 245 ft from the point where the brakes are applied, will the car hit the deer?
Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way. X 37 47 57 67 77 87 y 8. 10 14 28 44 n USE SALT Complete parts (a) through (e), given Ex = 372, Ey : 109, Σχ 24814, Σγ, 3105, Σχy 8053, and r z 0.9230. (a) Draw a scatter diagram displaying the data. 50 Graph Layers Clear All 45 Point 1 Delete 40 Point 2 Fill 35 Point 3 30 Point 4 25 Point 5 20 No Solution 15 Point 6 10 Point 7 Point 8 30 35 40 45 50 55 60 65 70 75 80 85 90 Help WebAssign. Graphing Tool Submission Data (b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Σχ - Ey = Ex?
Please answer the whole question (2) Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way. x 37 47 57 67 77 87 y 5 8 10 15 27 44 Complete parts (a) through (e), given Σx = 372, Σy = 109, Σx2 = 24814, Σy2 = 3079, Σxy = 8043, and r ≈ 0.927. (a) Draw a scatter diagram displaying the data. Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two…
A rehabilitation counselor believes that an increase in the number of social visits to a patient over the course of a week in the hospital will increase the patient's daily levels of positive mood. The counselor ensures that patients are limited to only three people during each visit. What is the alternative hypothesis for this relationship? A. H1 : ρ < 0 B. H1 : ρ > 0 C. H1 : r < 0 D. H1 : r ≤ 0
A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+5 mg/dl and σ=5+1 mg/dl. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: Once? n=5+2 times n=5+4 times Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.
The second slide is the first part of the question and the first slide is the second part of the question
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When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table: Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07 Let xx represent the flow rate variable and yy represent the variable for soil eroded. Then \bar x = 1.73, s_x = 1.38, \bar y = 2.81, s_y = 1.99xˉ=1.73,sx=1.38,yˉ=2.81,sy=1.99 Use this to complete the following calculation of the correlation coefficient for these data. r = \frac{1}{n-1}\left[\left(\frac{x_1 - \bar x}{s_x}\right)\left(\frac{y_1 - \bar y}{s_y}\right) + \left(\frac{x_2 - \bar x}{s_x}\right)\left(\frac{y_2 - \bar y}{s_y}\right) + \cdots + \left(\frac{x_n - \bar x}{s_x}\right)\left(\frac{y_n - \bar y}{s_y}\right)\right]r=n−11[(sxx1−xˉ)(syy1−yˉ)+(sxx2−xˉ)(syy2−yˉ)+⋯+(sxxn−xˉ)(syyn−yˉ)]…
A gardener applied chemical "Z" to plants in a flower bed. (S)he observed that the plants grew dramatically during the next two weeks. Using only the information from the previous two sentences, write a hypothesis about the effect of chemical "Z" on plants. (Note: Your hypothesis must be a testable statement.) A researcher conducted a series of experiments to test the effect of chemical “Z” on plants. The data from the experiments is summarized in the graph below. (Image of the Graph attached.) Interpret the graph above. What did the researcher learn about the effect of chemical “Z?” Based on the researcher’s graph, what can you conclude about the hypothesis you wrote for Question 7 above?
The correlation between X and Y is r = 0.35. If we doublw each X value, decrease each Y by 0.20, and interchange the variables (put X on the Y-axis and vice versa), the new correlation is?

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