Linear regression is applied for a supervised learning problem with a trainingdataset with m=84 observations. The training dataset records, for eachobservation, n=D9 input features, as well as one output. One performs a t-test in order to decide whether the 7th input feature is significant forpredicting the output. For this purpose, one computes the t-score:07toSE(Ô7)%3DThe residual standard error (RSE) is used to estimate o.Under which t-distribution is one to interpret the valuer of the t-scoreabove? (Note that a t-distribution is identified by the number of degrees offreedom).

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Answered: Linear regression is applied for a…

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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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
A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y = -13258.594 + 2.422X,, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000 20000 -20000 -20000 -40000 40000 TO 20 Index Normal Quantile Residuals vs. Program Per-Year Tuition ($) Residuals Predicted Values vs. Residuals Predicted Values 20000 140000- 120000- 100000 80000- -20000 60000 -40000 40000- 30000 50000 4000 Program Per-Year Tuition ($) 20000 60000 70000 -20000 20000 Residuals ..... a) To evaluate whether the assumption of linearity…
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In multiple regression analysis involving 10 independent variables and 100 observations, the critical value tt for testing individual coefficients in the model will have:A. 10 degrees of freedomB. 89 degrees of freedomC. 100 degrees of freedomD. 9 degrees of freedom In a multiple regression analysis involving 40 observations and 5 independent variables, the total variation SST=350 and SSE=50. The multiple coefficient of determination is:A. 0.8469B. 0.8529C. 0.8408D. 0.8571
A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…
The following output is from a multiple regression analysis that was run on the variables FEARDTH (fear of death) IMPORTRE (importance of religion), AVOIDDTH (avoidance of death), LAS (meaning in life), and MATRLSM (materialistic attitudes). In the regression analysis, FEARDTH is the criterion variable (Y) and IMPORTRE,AVOIDDTH, LAS, and MATRLSM are the predictors (Xs). The SPSS output is provided below, followed by a number of questions. Descriptive Statistics Mean Std. Deviation N feardth 27.0798 8.08365 163 importre 5.8282 2.46104 163 avoiddth 18.5460 6.97633 163 Las 70.1288 9.89460 163 matrlsm 53.5552 10.21860 163 Model Variables Entered Variables Removed Method 1 matrlsm, avoiddth, importre, lasa . Enter a. All requested variables entered. b. Dependent Variable: feardth Model Summary Model R R Square Adjusted R Square…
The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.
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(
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A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y; = -13258.594 + 2.422X;, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000- 20000 0. -20000 -20000 a) To evaluate whether the assumption of linearity has been violated, which of the following graph shou be examined? A. Predicted Values vs. Residuals B. Residual index plot C. QQ plot of residuals D. Residuals vs. Progrm Per-Year Tuition ($) b) To evaluate whether the assumption of normality has been violated, which of the following graph…
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x=3.8333, sx=2.4014, y=3.6500, sy=1.7942, and r=−0.9539, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a).

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