In fitting a multiple linear regression model of the form: E(Y)=B0 +B1X1 +B2X2+B3X3, if we use a sample size of n=20 then the number of degrees of freedom for SSyy will be: а. 17 b. 16 с. 18 d. 19 In fitting a multiple linear regression model of the form: E(Y)=B0 +B1X1 +B2X2+B3X3 , i we use a sample size of n=21 then the number of degrees of freedom for the regression model will be: а. 17 b. 18 O c. 20 d. 3

In fitting a multiple linear regression model of the form: E(Y)=B0 +B1X1 +B2X2+B3X3, if we use a sample size of n=20 then the number of degrees of freedom for SSyy will be: а. 17 b. 16 с. 18 d. 19 In fitting a multiple linear regression model of the form: E(Y)=B0 +B1X1 +B2X2+B3X3 , i we use a sample size of n=21 then the number of degrees of freedom for the regression model will be: а. 17 b. 18 O c. 20 d. 3

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

lecturer would like to know if the foundation Cumulative Grade Point Average (CGPA) predicts the undergraduate CGPA of engineering students at year one. She obtained the relevant information from 105 randomly selected students as follows: Σy = 333.15, Σxy = 1043.626, = 1021.487, > y² = 1077.836 %| Σ %3D (i) Obtain the least square regression line, ŷ = a + bx for the study. (ii) Estimate the strength of the association between the foundation CGPA and CGPA in year one. Interpret the result.
1. Consider the normal linear regression model Y~ N(a + Bx, o²). Data pairs (xi, yi) of 43 have been collected and summarised below: sample size n n Σ Xi = i=1 = n n n n 11.3, Σx = 154.8, Σy = 19.2, Συ = 135, & Σαϊyi £x i=1 i=1 i=1 i=1 24.9. From this data, compute the least-squares estimates for a and B. Given that the residual variance estimate is s² = 0.0544, evaluate the expected value and 95% prediction interval a future response Yo at xo = 10. Clearly state the definitions/formulas you are using in this question and report the pre- dicted value and interval correct to 2 decimal places. From the given information, provide a brief comment about this prediction.
Suppose you want to test whether X2 and X3 can jointly explain Y in the following regression model: Y = Bo + B1X1 + B,X2 + B3X3 + u You obtain data for 85 observations and conduct a joint test of significance at 1% level. Your restricted model is given by, OY = Bo + B3X3 +u OY = Bo + B1X1 + B3 X3 + u OY = Bo + B1X1 + u OY = Bo + u
A seafood-sales manager collected data on the maximum daily temperature, T, and the daily revenue from salmon sales, R, using sales receipts for 30 days selected at random. Using the data, the manager conducted a regression analysis and found the least-squares regression line to be Rˆ=126+2.37T. A hypothesis test was conducted to investigate whether there is a linear relationship between maximum daily temperature and the daily revenue from salmon sales. The standard error for the slope of the regression line is SEb1=0.65. Assuming the conditions for inference have been met, which of the following is closest to the value of the test statistic for the hypothesis test? t=0.274 A t=0.65 B t=1.54 C t=3.65 D t=193.85 E
4. We would like to determine how a man's weight can be used to predict his systolic blood pressure. We measure the weights (in pounds) and the systolic blood pressures of a sample of 17 men. The data are plotted on a scatterplot and it can be seen that a linear relationship is a reasonable assumption. The least squares regression line is calculated to be ŷ = 125.561 + 0.145x. The ANOVA table (with some values missing) is shown below: |Source of Variation | df | Sum of Squares Mean Square F Regression Error Total 26.46 617.82 (a) We would like to test whether a linear relationship exists between a man's weight and his systolic blood pressure. We will conduct an analysis of variance to test Ho: B1 = 0 vs. Ha: B1 + 0 at the 5% level of significance. Enter all missing values in the ANOVA table. Calculate the value of the test statistic, find the P-value of the test and provide a properly worded conclusion. (b) What is the value of the correlation between weight and systolic blood pressure…
Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.
A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y(kilograms) and the weekly time spent working out under the guidance of a trainer x(minutes). The resulting least-squares regression line for the study is y=2.04 + 0.12x A) predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. B)Predictions using this equation will be faily good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out C)Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out D) Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent…