5 You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors inparentheses below coefficient estimates):y 97.25 +33.74* x(3.86) (9.42)You want to test the following hypothesis: HD: 32= 12, H1: B2 12. If you choose to reject the null hypothesis based on these results, the probability youhave committed a Type li error is,between .05 and.100 between ,01 and .025O between .02 and .05impossible to determine without knowing the true value of 32

Given that: The linear regression equation is given as, y=97.25+33.74x 3.86 9.42 State the…

Answered: You estimate a simple linear regression…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
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.
In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?
Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: ß1 = 0 and the alternative hypothesis Ha: ß1 ? 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?
Consider the following model:? = ?? + ?,known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term. Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.
A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21 Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.
You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. What is the critical value of the test statistic (tc) if you want to perform a test for the significance of a single right-hand side (explanatory) variable at α = 0.05? a.) 2.023 b.) 2.708 c.) 2.423 d.) 2.704
1) What is the probability of a stroke over the next 10 years for John Smith, a 68-year-old smoker who has blood pressure of 175? What action might the physician recommend for John to reduce the risk of stroke? 2) Is there any multicollinearity problem in the above multiple regression model? How do you know?
Given a regression equation ?) = 2.35 + 6.82x, with n = 18 and a correlationcoefficient, r = 0.42, conduct a hypothesis test to determine if the regressionrelationship between x and y is statistically significant at the 2% level ofsignificance. What conclusion can be drawn from the hypothesis test?
In a data set with 12 observations, you try fitting two regression models. The esti-mated models are summarized as: Model 1: Y(hat) =3.5 + 2x; SSR= 5, and SSE= 10;Model 2: Y(hat) =3.0 + 1.5x + 0.4^2; SSR=23, and SSE=7 (a) Calculate R2 for both models. b. for both models test the null hypothesis that all the regression coefficients other than the intercept are 0.
The Mayor of texas whom is partners with a local agriculturalist wants to know how the amount of fertilizer and the amount of water given to plants affect their growth. The results were inputted into MINITAB so as to fit the model a) Write out the regression equation b) What is the sample size used in this investigation? c) Determine the values of *, ** and ***, **** d) Conduct a hypothesis test, at the 5% level of significance, to determine whether ? is significant. e) What would be the growth of the plant if 4g of fertilizer and 7g of ater was given to it daily? f) Carry out an F -test at the 1% significance level to determine whether the model is significant
Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.

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