The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation,(b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use theregression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126.DRedshiftDistance0.02370.320.05450.750.07241.020.03970.560.04420.610.01030.16a. Find the explained variation.(Round to six decimal places as needed.)b. Find the unexplained variation.(Round to six decimal places as needed.)c. Find the indicated prediction interval.billion light-years

Given data: Redshift 0.0237 0.0545 0.0724 0.0397 0.0442 0.0103 Distance 0.32 0.75 1.02 0.56…

Answered: The table below lists measured amounts…

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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The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126. Redshift Distance a. Find the explained variation. 0.0237 0.34 (Round to six decimal places as needed.) 0.0541 0.75 0.0723 0.98 C 0.0397 0.57 0.0444 0.62 0.0103 0.13
The data shown below are the initial weights and gains in weight (in grams) of female rats on a high protein diet from 24 to 84 days of age. The point of interest in these data is whether the gain in weight is related to (dependent on) the initial weight. If so, then feeding experiments on female rats can be made more precise by adjusting for differences in initial weights of the rats. Statistically test this with a regression analysis. Rat Number Initial Weight (gms) Weight Gain (gms) 1 50 128 2 64 159 3 76 158 4 64 119 5 74 133 6 60 112 7 69 96 8 68 126 9 56 132 10 48 118 11 57 107 12 59 106 13 46 82 14 45 103 15 65 104 I used excel's regression took pak and got the following: SUMMARY OUTPUT Regression Statistics Multiple R 0.489416452 R Square 0.239528464 Adjusted R Square 0.181030653 Standard Error 8.869929833 Observations 15…
The following estimated regression equation based on 10 observations was presented. ŷ = 28.1270 + 0.6906x, + 0.3980x2 (a) Develop a point estimate of the mean value of y when x, = 170 and x2 = 350. (b) Develop a point estimate for an individual value of y when X1 = 170 and X2 = 350.
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude 8 15 22 28 31 33 Temperature 56 39 24 - 28 - 41 - 60 a. Find the explained variation. (Round to two decimal places as needed.)
A particular article used a multiple regression model with the following four independent variables. y = error percentage for subjects reading a four-digit liquid crystal displayx1 = level of backlight (from 0 to 122 cd/m)x2 = character subtense (from .025 to 1.34)x3 = viewing angle (from 0 to 60)x4 = level of ambient light (from 20 to 1500 lx) The model equation suggested in the article is given below. (a) Assume that this is the correct equation. What is the mean value of y when x1 = 30, x2 = 0.6, x3 = 50 and x4 = 150?(b) What mean error percentage is associated with a backlight level of 40, character subtense of 0.6, viewing angle of 20, and ambient light level of 30?
Section 10.3 Question #6 Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude 4 11 14 20 28 31 34 Temperature 55 39 26 −2 −34 −41 −59 a. Find the explained variation. ______________ (Round to two decimal places as needed.) b. Find the unexplained variation. _______________ (Round to five decimal places as needed.) c. Find the indicated prediction interval. _____________°F < y < ____________ °F (Round to four decimal places as needed.)
A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.3 14.9x Coefficients (Intercept) X Estimate St 4.3 Ho: B₁ = 0 Ha: B₁ > 0 B1 O Ho: B₁ Ha: B₁ <0 = 0 14.9 B1 O Ho: B₁ = 0 0 Ha: B1 Std. Error Test statistic P-value 2.9 5.1 1.48 Specify the null and the alternative hypotheses that you would use in order to test whether a negative linear relationship exists between x and y. 2.92 0.08 0.01
A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does thecorrelation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for therelationship between length of an aspen leaf and its surface area? (A) The value must be exactly 1 or to indicate a linear model is the most appropriate model. (B) The value must be 0 to indicate a linear model is the most appropriate model. (C) A causal relationship should be established first before determining the most appropriate model. (D) The value of 0.94 implies that only 88% of the data have a linear relationship. (E) Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.
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?
The estimated regression equation for a model involvingtwo independent variables and 55 observations is: y-hat = 55.17 + 1.1X1 - 0.153X2 Other statistics produced for analysis include: SSR = 12370.8 SST = 35963.0 Sb1 = 0.33 Sb2 = 0.20 a) Interpret b1 and b2 in this estimated regression equation b. Predict y when X1 = 55 and X2 = 70. b) Compute R-square and Adjusted R-Square. e. Compute MSR and MSE. f. Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05). g. Perform a t test using the critical value approach for thesignificance of β1. Use a level of significance of 0.05. h. Perform a t test using the critical value approach for thesignificance of β2. Use a level of significance of 0.05.
Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is: kids; = Bo + B1educ; + uż. 1. What are the parameters in the model? 2. What kinds of factors are contained in u? Are these likely to be cor- related with level of education? 3. Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.
The data below is for a hypothetical study investigating the Systolic Blood Pressure (SBP) of construction workers. The table shows respective measurements of 20 workers along with hours of work per day and the area of the city the work took place. [You can use Excel-Data Analysis – Regression or http://vassarstats.net/multU.html] SBP Hrs/day Area 109.6 7 east 107.4 8 east 140.3 9 east 146.5 12 east 98.2 6 east 137.8 9 east 124.1 10 east 113.2 8 east 127.8 9 east 125.3 8 east 108.5 6 west 181.3 13 west 137.4 10 west 146.2 10 west 142.4 9 west 123.7 8 west 129.6 8 west 143.6 9 west 160.7 11 west 148.3 9 west a) What is the regression equation? b) Interpret the meaning of the slopes in this problem. d) At the 0.05 level of significance, determine whether each independent variable makes a contribution to the…

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