In Lab #12 you will collect data on the photosynthesis rates ofgoldenrod leaves measured at 8 different light intensities.Suppose you obtained the following regression output from R:Coefficients:Estimate Std. Error t value Pr(>Itl)(Intercept)light_intensity 0.048806 0.002952 16.531 3.12e-06 ***-1.958056 0.617541 -3.171 0.0193Signif. codes: 0 **0.001 *** 0.01 **' 0.05 '.' 0.1 ' ' 1What would the 99% confidence interval be for the slope (i.e.,light_intensity)?[Hint: Remember to calculate the proper degrees of freedom!]O (0.0416, 0.0560)O (0.0389, 0.0587)O (0.0385, 0.0591)O (0.0395, 0.0581)O (0.0379, 0.0598)

Given : b1 = 0.048806 Se = 0.002952

Answered: In Lab #12 you will collect data on 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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1. You estimated a regression with the following output. Source | SS df MS Number of obs = 210 -------------+---------------------------------- F(1, 208) = 940.28 Model | 5529353.01 1 5529353.01 Prob > F = 0.0000 Residual | 1223155.7 208 5880.55624 R-squared = 0.8189 -------------+---------------------------------- Adj R-squared = 0.8180 Total | 6752508.71 209 32308.6541 Root MSE = 76.685 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 13.66711 .4457062 30.66 0.000 12.78843 14.54579 _cons | 103.7139 41.86814 2.48 0.014 21.17362 186.2542…
Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. What is the subpopulation mean when x = 7 servings per day?
Suppose a data set of 200 observations (n = 200) was analyzed using OLS to examine the relationship between CEO salary and various measures of firm performance. The regression results are as follows, with standard errors in parentheses: logy = 5 + 0.2logx₁0.03x₂ +0.002x3 (0.2) (0.04) (0.004) where? (0.009) y = CEO salary in thousands of dollars X₁ = annual firm sales X₂ = percentage of sales lost to competitors X3 = return on stock in percent R² = 0.290 Suppose you want to test the null hypothesis that percentage of sales lost to competitors has no ceteris paribus effect on the salaries of CEOS. For the one-sided alternative hypothesis ß₂ < 0 and 1% rejection rule (i.e., at the 1% level), you would_ the null hypothesis that ß₂ = 0.
A particular article presented data on y = tar content (grains/100 ft³) of a gas stream as a function of x₁ = rotor speed (rev/min) and x₂ = gas inlet temperature (°F). The following regression model using X₁, X2, X3 = ×₂² and ×4 = X₁X₂ was suggested. (mean y value) = 86.5 – 0.121x₁ +5.07x2 - 0.0706x3 + 0.001x4 (a) According to this model, what is the mean y value (in grains/100 ft³) if x₁ = 3,400 and x₂ = 55. grains/100 ft³ (b) For this particular model, does it make sense to interpret the value of ₂ as the average change in tar content associated with a 1-degree increase in gas inlet temperature when rotor speed is held constant? Explain. Yes, since there are no other terms involving X2. O Yes, since there are other terms involving X₂. ● No, since there are other terms involving X2. O No, since there are no other terms involving X2.
The article "The Undrained Strength of Some Thawed Permafrost Soils"+ contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x₁ = depth (m) x₂ = water content (%) The predicted values and residuals were computed using the estimated regression equation y = -156.50 - 16.52x₁ + 13.83x₂ + 0.100x3 -0.258x4 +0.496x5 ₁², x₁ = x₂², and x5 = X1X2• where x3 = y X1 14.7 8.8 31.4 48.0 36.5 26.9 25.6 36.9 25.8 x2 10.0 6.2 39.2 16.0 6.8 39.3 20.7 16.8 7.0 38.4 7.4 33.8 38.8 8.3 33.9 16.9 6.4 27.0 8.1 33.2 24.9 10.0 12.8 28.0 16.0 4.4 26.2 37.9 7.3 2.8 34.7 1.9 36.5 Predicted y 22.86 46.10 27.38 11.23 13.47 16.80 23.55 25.24 15.75 24.47 15.19 29.93 15.51 8.00 Residual -8.16 1.90 -1.78 -1.23 2.53 0.00 -2.85 13.56 1.15 2.53 0.81 -5.03 -8.21 4.80 (a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.) SSTO = SSResid = SSRegr = (b) Calculate R² for this regression model. (Round your answer to three decimal…
10. You estimated a regression with the following output. Source | SS df MS Number of obs = 333 -------------+---------------------------------- F(1, 331) = 4608.21 Model | 32636494.1 1 32636494.1 Prob > F = 0.0000 Residual | 2344225.8 331 7082.25316 R-squared = 0.9330 -------------+---------------------------------- Adj R-squared = 0.9328 Total | 34980719.9 332 105363.614 Root MSE = 84.156 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 30.79902 .4537022 67.88 0.000 29.90652 31.69153 _cons | 20.85313 42.1964 0.49 0.621 -62.1538 103.8601…
The US government is interested in understanding what predicts death rates. They have a set of data that includes the number of deaths in each state, the number of deaths resulting from vehicle accidents (VEHICLE), the number of people dying from diabetes (DIABETES), the number of deaths related to the flu (FLU) and the number of homicide deaths (HOMICIDE). Your run a regression to predict deaths and get the following output: At α = .10, which variable(s) is/are significant predictors of deaths?
This table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 22.1370 + 0.5303Xq + 0.4920X2 (a) Interpret b₁ in this estimated regression equation. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₁ when X₂ is held constant. O b₁ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. O b₁ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Interpret b₂ in this estimated regression equation. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 22.1370 is an estimate of the change in y corresponding to a…
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