Answered: Tristan has completed his STAT 1342…

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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Data from 147 colleges from 1995 to 2005 (Lee,2008) were tested to predict the endowments (in billions) to a college from the average SAT score of students attending the college. The resulting regression equation was Y = -20.46 + 4.06 (X). This regression indicates that: a. for every one-point increase in SAT scores, a college can expect 4.06 billion more in endowments. b. most colleges have very high endowments. c. for every one-point increase in SAT scores, a college can expect 20.46 billion fewer in endowments. d. for every one-dollar increase in endowments, the college can expect a half-point increase in SAT scores.
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X1), the annual income of the family (X2), and the number of times the family went out on an outing in the last year (X3). She collects data from 196 families and estimates the following regression: Y=120.45+1.54X1+2.12X2+2.12X3. Suppose β1, β2, β3, denote the population slope coefficients of X1, X2, and X3, respectively. The researcher wants to check if neither X1 nor X2 have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (H0: β1=0, β2=0 vs. H1: β1≠0 and/or β2≠0) to be 3.00. The p-value for the test will be enter your response here?
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…
You have gathered data from a random sample of fast-food sandwiches in order to better understand how the amount of fat in these sandwiches relates to the amount of carbohydrates in the sandwiches. Your ultimate goal is to construct a regression equation to predict amount of carbohydrates based on amount of fat. If this is your goal, which variable should you put on the vertical axis (or y-axis) of a scatterplot of this data? O When conducting a regression analysis, it makes no difference which variable is on which axis. O Amount of fat, because it is the explanatory variable. O Amount of carbohydrates, because it is the explanatory variable. Amount of carbohydrates, because it is the response variable. O Amount of fat, because it is the response variable.
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were: y=ax+b a=-1.383 b=24.599 r2=0.962361 r=-0.981 Use this to predict the number of situps a person who watches 5.5 hours of TV can do (to one decimal place)
A particular article used a multiple regression model to relate y = yield of hops to x, = average temperature (°C) between date of coming into hop and date of picking and x, = average percentage of sunshine during the same period. The model equation proposed is the following. y = 415.11 – 6.6x1 – 4.50x2 +e (a) Suppose that this equation describes the actual relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40? (b) What is the mean yield when the average temperature and average percentage of sunshine are 19 and 44, respectively?
A particular article used a multiple regression model to relate y = yield of hops to x₁ = mean temperature (°C) between date of coming into hop and date of picking and x₂ = mean percentage of sunshine during the same period. The model equation proposed is the following. y = 415.116.6x₁4.50x2+e (a) Suppose that this equation does indeed describe the true relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 39? (b) What is the mean yield when the mean temperature and percentage of sunshine are 19.1 and 42, respectively? You may need to use the appropriate table in Appendix A to answer this question.
In calculating a simple regression for average number of drinks consumed (x) and grade point average (y), you get a slope coefficient (b) of -.15 and a y intercept of 2.50. Using the formula Y = a + bX, what would the predicted grade point average be for a student who averaged 1.0 drinks per week?
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x₁) and newspaper advertising (x₂). The estimated regression equation was ŷ = 83.5+ 2.21x₁ + 1.80x₂. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.495. (a) Compute and interpret R² and R2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R² = 0.653 and R2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis ---Select--- preferred since both R² and R2 show ---Select--- ✓percentage of the variability of y explained when both independent variables are used. . Adjusting for the number of…
Tristan has completed his STAT 1342 course. He intends to build a simple linear regression model using control variable (X) as number of hours per week for his preparations and (Y) as the weekly performance measured in a 100-point scale and based on his self-assessment. There were totally n = 28 weekly collected records. The model built by Tristan was: Ý = 10 + 7· X with the standard error of estimated slope equal to SE = SE [6] = 2.8 1. At the significance level, a = 0.01, is there sufficient evidence that X positively impacts Y? • Evaluate Test Statistic • Specify critical value (or values) for this procedure • State the Rejection Rule • Formulate your decision 2. Estimate the population slope (= B) with confidence level, C = 0.95 • Specify critical value (or values) for this procedure • Evaluate UCL and LCL Solution 10
Define both x and y in all problems. x is the cause, and y is the effect. This is the most important step when doing linear regression, otherwise, all the remanding parts will be wrong.

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