5. (3) Indicate if each of the following statements about the simple linear regression modeltrue or false and explain why(a). The simple regression line estimated by the method of Least Squared passes through thesample mean of dependent and independent variable.(b). The slope estimator of the Least Squares regression line is free of measure.(c). The sample covariance between the residuals from the least square regression and theexplanatory variable is zero.(d). If the values of x more widely spread out, the estimate of the slope coefficient is less concise.(e). Adjusted R-squared will always increase when an additional independent variable is added intothe regression.

The simple linear regression model shows the relationship b/w 1 independent variable and 1 dependent…

Answered: 5. ( 3) Indicate if each of the…

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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4. The following regression is fitted using variables identified that could be related to tuition charges ($) of a university. TUITION = a+ B ACCEPT + y MSAT + 1 VSAT Where ACCEPT = the percentage of applicants that was accepted by the university, MSAT = Median Math SAT score for the freshman class and VSAT = Median English SAT score for the freshman class. The data was processed using MNITAB and the following is an extract of the output obtained: Predictor Coef StDev T P Constant -26780 6115 -4.38 0.000 ACCEPT 116.00 37.17 * 0.003 MSAT -4.21 14.12 VSAT 70.85 15.77 -0.30 4.49 0.767 ** S = 2685 R-Sq = 69.6% Analysis of Variance R-Sq (adj) = 67.7% Source DF SS MS F P Regression 3 808139371 Residual Error 49 353193051 269379790 7208021 37.37 0.000 Total 52 1161332421 a) Write out the regression equation. b) State the dependent and independent variable(s) c) Fill in the blanks identified by ** and ****. d) Is B significant, at the 10% level of significance? e) State one limitation of using…
A pharmaceutical company is examining the relationship between dosage of a new pain-relief medication and the time it takes for patients to experience pain relief from a headache. Various dosages ranging from 200 to 1,200 milligrams (mg) in 100-milligram increments were given to 41 randomly selected patients, and the time until relief was measured in minutes. A check of the conditions necessary for inference for the slope of a regression line shows that they are met. A 95 percent confidence interval for the slope of the regression line relating the dosage, x, to the time until relief, y, is given by (−4.15,−2.27). Based on the confidence interval, which of the following claims is supported?
(e) Find the line of best fit (or, the regression line) for the following data points: (3,13)(3,13), (4,18)(4,18), (5,23)(5,23), and (7,24)(7,24).
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…
A pharmaceutical company is examining the relationship between dosage of a new pain-relief medication and the time it takes for patients to experience pain relief from a headache. Various dosages ranging from 200 to 1,200 milligrams (mg) in 100-milligram increments were given to 41 randomly selected patients, and the time until relief was measured in minutes. A check of the conditions necessary for inference for the slope of a regression line shows that they are met. A 95 percent confidence interval for the slope of the regression line relating the dosage, x, to the time until relief, y, is given by (−4.15,−2.27). Based on the confidence interval, which of the following claims is supported? A 100 mg increase in dosage results in a decrease in the time until relief by more than two minutes on average. A A 100 mg increase in dosage results in a decrease in the time until relief by more than four minutes on average. B There is not a linear relationship…
Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(
30)
You forgot to JUSTIFY THE ANSWRRS LAST TIME
- 16. Find the least squares regression line for the points (0, 8), (4, 5), (5, 3), (8,-1), and (10,-2). Round numerical values in your answer to two decimal places. a. y=-1.07x+2.63 b. y=-1.27x+8.36 c. y=-1.07x+8.36 d.y=-1.07x+10.54 c. y=-1.27x+2.63
Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
The accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative trend; therefore the Normality condition is satisfied.D.The residual plot shows no trend; therefore the Normality condition is not satisfied.

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