8. If all the points in a scatter diagram lie on the least squares regression line, then thecoefficient of correlation:a. Must be 1.0b. Must be -1.0c. Must be either 1.0 or -1.0d. Must be 09. In simple linear regression, the correlation coefficient r and the least squares estimate ofthe population slope:a. Must have the same numerical valueb. Must have opposite signsc. Must have the same signd. May have opposite signs or the same signFILL IN THE BLANKS:10.provides a "best-fit" mathematical equation for the values oftwo variables x and y.11. The symbol for the independent variable isand the symbol forthe dependent variable is12.measures the strength of the relationship betweenthe dependent and independent variables.13. One way to examine whether two variables might be linearly related is to construct a14. The assumption of equal standard deviations about the regression line is called

Here As PER POLICY I SHOULD HAVE TO CALCULATE FIRST QUESTION ONLY EVEN THOUGH I HAVE CALCULATED MORE…

Answered: 8. If all the points in a scatter…

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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In order to determine the relationship between the number of units sold of a company's product (y) in 9 cities with their major competitor's price (*1) in dollars, and the number of stores (r2) the competitor has in each city, the following data were collected. Competitor Competitor Units sold Price Stores 550 35 3 545 35 3 540 40 600 40 2 600 44 3 510 35 570 39 4 650 45 1 615 45 3 Generate a linear multiple regression output for the data. a) Report the regression coefficients accurate to 3 decimal places: ŷ= b) Report the coefficient of determination accurate to 3 decimal places: R
In the simple linear regression model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be a) close to either -1 or +1 b) close to zero c) close to -1 d) close to +1 ( don't hand writing solution)
Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 88 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−0.813+0.177?,h^=−0.813+0.177w, with standard error for the coefficient of ?w equal to 0.448. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
Determine if the statement is true or false.
9. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y 160 130 330 120 70 190 (a) x = 170 calories (c) x = 150 calories 180 (b) x = 80 calories 420 470 360 250 530 (d) x = 210 calories Find the regression equation. x+( (Round to three decimal places as needed.) y = Choose the correct graph below. OA. О В. OC. OD. 560- 560 560 560- 200 G 0IN T> 200 200 Calories Calories Calories Calories (a) Predict the value of y for x = 170. Choose the correct answer below. O A. 411.632 O B. 543.752 O C. 455.672 O D. not meaningful (b) Predict the value of y for x = 80. Choose the correct answer below. O A. 411.632 О В. 257.492 O C.…
2. A sample of small cars was selected to attempt to use the horsepower (x) in hp of the car to predict the fuel efficiency (y) in miles per gallon. A researcher fitted a linear regression model. ŷ-44.0 -0.150x a) Interpret the slope of the regression line. b) Find the predicted fuel efficiency for a horsepower of 150 hp? c) If the fuel efficiency for a car of horsepower of 150hp had an actual fuel efficiency of 25mpg, what is the residual (error) for this car? d) Calculate the correlation coefficient. e) What is the strength of the correlation coefficient? R²=68% f) Interpret the y-intercept.
Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 85 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−4.273+0.834?,h^=−4.273+0.834w, with standard error for the coefficient of ?w equal to 0.242. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
I. Show complete solutions. Simple Linear Regression and Correlation: a.) Results of a study on the occurrence of sodium and chloride in surface streams in a coastal area. The following data are chloride concentration (y) in mg/liter and road-way area in the watershed (x) in %. Y 0.24 4.6 1. What is the value of the correlation coefficient? 2. What is the interpretation for this case? 3. What is the estimated chloride concentration if road way 0.3 6.4 0.45 9.8 area in the watershed is 1.30% 0.75 10.7 4. What is the equation of the prediction line? 0.57 10.6 0.75 10.9 0.4 11.7 0.8 12.5 0.6 14 0.78 14.7 0.85 15.1 0.68 18.3 0.69 19.2 1.4 23.1 1.15 27.3 1.05 27.7 1.69 32 1.62 38.4
The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.972. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y= - 0.0070x + 44.4405. Complete parts (a) and (b) below. Click the icon to view the data table. ..... (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. Data Table (Round to one decimal p Full data set gas mileage Miles per Weight (pounds), x Weight (pounds), x Miles per Gallon, y Car Car Gallon, y…
The following table contains ACT scores and the GPA for eight college students. Estimate the relationship between GPA (yi) and ACT (x;) using OLS regression by hand. Report the intercept and slope estimates: Student 1 2 3 4 5 6 7 8 GPA 2.8 3.4 3.0 3.5 3.6 3.0 2.7 3.7 ŷ₁ =B₁ + B₁x₁ ACT 21 24 26 27 29 25 25 30 y X ŷ₁
A shop manager paid local radio stations to air a sales advertisement for one weekend. Since they charged different fees, there was a variation in the number of times the advertisement was aired. (Assume all stations are similar in contents). After that sales weekend, the manager wants to find out whether there is any linear association between the number of times the sales advertisement was aired at local radio stations and the sales figures in that weekend. Compute for the Correlation Coefficient (r). Find the regression equation. Then solve for: a) The sales if the number of airings is 8. b) The number of airings required to have a sales of 27,000 pesos. 1. r = Blank 1 2. y = Blank 2 + Blank 3 x a) Blank 4 pesos b) Blank 5 airings

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