4. Suppose that n=100 i.i.d observations for (Y₁, X₁) yield the following resultsỸ = 32.1 +66.8X, SER=15.1, R² = 0.81(15.1) (12.2)Another researcher is interested in the same regression, but he makes an error when he enters the datain his regression program: He enters each observation twice, so he has 200 observations. Using these200 observations, what results will be produced by his program? Write it in the following format:Ỹ+---X, SER=(---) (---)R² =

Answered: Image /qna-images/answer/ee988aa9-9d58-4c7d-978f-ebd9ead3fb10.jpg

Answered: Ŷ = 32.1 +66.8X, SER=15.1, R² = 0.81…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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Similar questions

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X,), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (X). She collects data from 152 families and estimates the following regression: Y = 120.45 + 1.12X, + 2.12X2 + 1.98X3 Suppose B1. B2, B3, denote the population slope coefficients of X, X2, and X3, respectively The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B, = 0, B2 = 0 vs. H B, 0 and/or Bz 0) to be 3.00. The p-value for the test will be (Round your answer to two decimal places.) At the 10% significance level, we will the null hypothesis. reject fail to reject Enter your answer in…
Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?
Suppose that n = 50, i.i.d observations for (Y₁, X₁) yield the following regressions results: Ỹ= 49.2 + 73.9 X, SER = 13.4, R²=0.78 (23.5) (16.4) Another researcher is interested in the same regression, but makes an error when entering the data into a regression program: The research enters each observation twice, ending up with 100 observations (with observation 1 entered twice, observation 2 entered twice and so forth). Using these 100 observations, what results will be produced by the regression program? Complete the spaces in the equation below. Report the intercept and slope to one decimal place, but report the R2 to two decimal places. Ŷ = + * X, R² =
The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X,), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (X3). She collects data from 152 families and estimates the following regression: Ỹ = 146.34 + 1.54X, + 1.05X2 +2.12X3. Suppose B1, B2, ß3, denote the population slope coefficients of X,, X,, and X3, respectively. The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X, constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B, = 0, B, = 0 vs. H,: B, #0 and / or ß, #0) to be 2.30. The p-value for the test will be (Round your answer to two decimal places.) At the 1% significance level, we will the null hypothesis.
The following estimated regression equation based on 10 observations was presented. Ỹ = 29.1370 + 0.5503×y + 0.4960xz Here, SST = 6,728.125, SSR = 6,226.375, 5,= 0.0817, and 5₂0.0565. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR= MSE = (b) Compute F and perform the appropriate F test. Use a = 0.05. State the null and alternative hypotheses. Ho: ₁0 and ₂ = 0 H₂: P₁ = 0 and ₂0 O ○ Ho: P₂ > 1₂ O H₂: P₂ SP₂ OH: A₂ = #0 and ₂0 H: One or more of the parameters is equal to zero. H₂: Pg 2 P₂ H₂: One or more of the parameters is not equal to zero. Find the value of the test statistic. (Round your answer to two decimal places.) F= Find the p-value. (Round your answer to three decimal places.) p-value= State your conclusion. Reject Ho. There is sufficient evidence to conclude that the overall model is significant. O Do not reject Ho- There is sufficient evidence to conclude that the overall model is significant. O Reject H. There is insufficient evidence to conclude…

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