### Table of Results| Variable | Coefficients | Standard Error | T Statistic | p-Value ||------------|--------------|----------------|-------------|---------|| Intercept | 11.680464 | 7.132097 | 1.64 | 0.1048 || Revenue | 0.6999226 | 0.321328 | 2.18 | 0.0319 || Efficiency | 0.8029396 | 0.077201 | 10.40 | <0.0001 |#### Explanation:This table presents a statistical analysis output. It includes:- **Variable**: The name of the variable being analyzed.- **Coefficients**: The estimated effect or contribution of each variable.- **Standard Error**: Indicates the variability of the coefficient estimate.- **T Statistic**: A measure used to evaluate the significance of the coefficient.- **p-Value**: Shows the probability that the observed results could have occurred under the null hypothesis. Lower p-values suggest higher statistical significance.#### Interpretation:- **Intercept**: Has a coefficient of 11.680464, with a standard error of 7.132097. The t statistic is 1.64 with a p-value of 0.1048, indicating it is not statistically significant at common alpha levels (e.g., 0.05).- **Revenue**: Shows a coefficient of 0.6999226, with a relatively larger standard error of 0.321328. It has a t statistic of 2.18 and a p-value of 0.0319, making it statistically significant at the 0.05 level.- **Efficiency**: Displays a coefficient of 0.8029396, with a small standard error of 0.077201. It has a very high t statistic of 10.40 and a p-value of less than 0.0001, indicating a high level of statistical significance. A nonprofit analyst is evaluating which variables to use for predicting nonprofit charitable commitment, representing how committed an organization is to its charitable purpose. The analysis involves two independent variables:1. **Revenue ($X_1$)**: Measured as total revenue in billions of dollars, this variable serves as an indicator of the size of the nonprofit.2. **Efficiency ($X_2$)**: This variable measures the percent of private donations remaining after fundraising expenses, serving as a measure of nonprofit fundraising efficiency.The dependent variable is:- **Commitment (Y)**: Measured as the percentage of total expenses allocated directly to charitable services.Both variables $X_2$ and $Y$ are represented as percentages. Data were collected from a random sample of 97 nonprofit organizations. The results are available in a table.**Task:**a. State the multiple regression equation. $\hat{Y}_i = \boxed{ } + (\boxed{ }) X_{1i} + (\boxed{ }) X_{2i}$ (Round to two decimal places as needed.)

It is given that the multiple regression output. We have Intercept = 11.680464 Revenue =…

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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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Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x 0 Test score, y 38 Find the regression equation. 2 3 3 4 6 45 50 49 61 68 0 (a) x = 2 hours (c) x = 15 hours (b)x=4.5 hours (d) x=2.5 hours y = X + (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)
b. Find the equation of the regression line for the minutes the actor appeared shirtless in a film and the film's opening weekend gross. y = ___x + ____(Round to two decimal places as needed)
Suppose Ms. Carr is interested in the relationship between her students' 9th grade math final exam scores and the number of hours they spent studying during the year. She collects information for 15 ninth grade students and uses it to obtain the regression equation, where ?x is the number of hours spent studying during the year and ?̂ is the predicted final exam score. ?̂ =1.48?+75.64 The scatter plot displays her results. What is the predicted ?̂ value when a student spends 13 hours studying? Round your answer to one decimal place. Select the correct interpretation. The above predicted value of ?̂ is the predicted final math test score if a student studies 13 hours during the year. the predicted score of 13 out of 15 students. what any student will score on the final exam if they study at least 13 hours. the math final test score that 13 students beat.
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. A horizontal table lists x-values in the first row and y-values in the second row. The x-values are as follows from left to right: 6, 8, 20, 28, and 36. The y-values are as follows from left to right: 2, 4, 13, 20, and 30. A. y with caret= −2.79 + 0.897x B. y with caret = −3.79 + 0.801x C. y with caret= −2.79 + 0.950x D. y with caret = −3.79 + 0.897x
Use the data below for the PHONES questions that follow. Data compiled from the CIA World Factbook, https://www.cia.gov/. The number of cell phones in use in a country can be approximated from the number of main lines in use in that country by using the regression equation yhat=25+3x which had an R² of about 90%. (The numbers here are millions. For example, "1.2" would represent 1.2 million or 1,200,000.) PHONES 1 At the time the data was collected, the USA had about 314 million cell phones in use and about 150 million main lines in use. What was the residual for the USA? Enter a number of millions. For example, if your answer is 2.85 million enter "2.85". Do not enter anything else such as symbols or words.
Fill in the blanks. a. Multicollinearity is considered to be severe if the VIF for one or more predictor variables is ______. or greater. b. If the coefficient of multiple determination for the regression of the predictor variable x11 on all the other predictor variables in a regression equation is 0.6, then the VIF for x1 is ______. c. The effect of multicollinearity in a polynomial regression analysis can be reduced by ______. the predictor variable.
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.3 8.5 y 13.4 7 3.6 2.6 2.2 2.6 0.8 11 10.2 7.4 6 5.7 6.3 4.9 * = thousands of automatic weapons y = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 10.1 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 9.9 thousand automatic weapons? Answer = Round to 3 decimal places.
Given: r1,= 0,28 r3; =0.49 rip=0,51 o, = 2.7 a,-24 a-2.7 Find the regression equation of x3 on x and x2
Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southem U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. Weekly Gross Revenue Television Advertising Newspaper Advertising ($100s) Market ($100s) ($100s) Mobile 102.5 5.1 1.6 Shreveport 52.7 3.2 3.0 Jackson 75.8 4.0 1.5 Birmingham 127.8 4.3 4.0 Little Rock 137.8 3.5 4.3 Biloxi 101.4 3.6 2.3 New Orleans 237.8 5.0 8.4 Baton Rouge 219.6 6.9 5.8 (a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) -43.258 O + 39.367 Test for a significant relationship between television advertising…
Use B = -15.812961, and ₁ = 0.096300 to determine the equation of the estimated regression line. (Round your numerical answers to four decimal places.) ŷ =

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Click the icon to view the table of results. a. State the multiple regression equation. ₁=+₁₁+x₂i (Round to two decimal places as needed.)