Concept explainers
Confidence Intervals for a Regression Coefficients A confidence interval for the regression coefficient β1is expressed as
b1 − E < β1 < b1 + E
where
The critical t score is found using n − (k + 1) degrees of freedom, where k, n, and
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Elementary Statistics (13th Edition)
- Noise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.arrow_forwardXYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?arrow_forwardOlympic 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?arrow_forward
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardFor the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracyarrow_forwardWhat will you conclude about a regression model if the Breusch-Pagan test results in a small p-value? a The model contains dummy variables The model contains homoskedasticty c. The model omits some important explanatory factors d. The model contains heteroskedastictyarrow_forward
- t test of a multiple regression model J OO D 3/5 Español Using 26 observations on each variable, a computer program generated the following multiple regression model. y = 85.8 + 8.05x, -2.61x,-2.41x,+7.77x4+8.05x5 If the standard errors of the coefficients of the independent variables are, respectively, 5.00, 2.53, 1.44, 6.48, and 3.82, can you conclude that the independent variable x, is needed in the regression model? Let B, B,, ., B, denote the coefficients of the 5 variables in this model, and use a two-sided hypothesis test and significance level of 0.10 to determine your answer. (a) State the null hypothesis H and the alternative hypothesis H,. H, 0 H, :0 (b) Determine the type of test statistic to use. Degrees of freedom: dfn: dfd:| O=0 OSO (c) Ft Chi-Square e test statistic. (Round to two or more decimal places.) (d) Find the two critical values at the 0.10 level of significance. (Round to two or more decimal places.) I and 0 (e) Can you conclude that the independent variable…arrow_forwardSolve for C and compute the residualarrow_forwardIn the regression model ŷ = a + bx, a and b are the: omitted variables O sample statistics O random variables O population parametersarrow_forward
- Estimate the number of server users y (employees) when the amount of memory storage used x (GB) is x = 15.4 in a time slot based on the regression line for your data. a. 30 employees b. 31 employees c. 32 employees d. 11.77 GBarrow_forwardConcept Exercise ő. I.I formal education received by each of his parents. It is An independent researcher is interested in finding out whether there exists a positive relationship between the number of years of formal education received by an individual and the number of years assumed that the number of years of formal education received by one parent of an individual is positively correlated with that of the other parent. The researcher randomly selects 250 individuals and estimates the following regression function: ŷ = 8 +0.56X,, where denotes the number of years of formal education received by the individual and X, denotes the number of years of formal education received by the h individual's father. Since the researcher only incorporates the educational attainment of an individual's father in the regression, and not that of the individual's mother, omitted variable bias will occur. Which of the following statements correctly describes the omitted variable bias? O A. Omitted…arrow_forwardThe least-squares regression equation is y = 602.1x + 17,023 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.6748. Complete parts (a) through (d). This is (Round higher CE lower Median Income 55000- 25000- 15 20 25 30 35 40 45 50 55 60 Bachelor's % (a) Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree. $32076 (Round to the nearest dollar as needed.) (b) In a particular region, 29.1 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,759. Is this income higher than what you would expect? Why? than expected because the expected income is lar as needed.) Q 0arrow_forward
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