Assume that we built a linear regression model with p 5 predictors. Determine the minimum number of observations n for which B when SE(B;) = 5.00. Consider a = 0.05. 13.05 is statistically significant |3D %3D
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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.Which of the following is not one of the statistical assumptions behind linear regression? a. The residuals should not be autocorrelated. b. The variance of Y for all combinations of X variable values should be constant. c. The X variables should be normally distributed. d. The residuals should be normally distributed.
- Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=10,815.11+2563.46(Education)+897.49(Experience)Estimated Salary=10,815.11+2563.46(Education)+897.49(Experience) Suppose two employees at the company have been working there for five years. One has a bachelor's degree (88 years of education) and one has a master's degree (1010 years of education). How much more money would we expect the employee with a master's degree to make?Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=10,737.30+2872.43(Education)+1129.1(Experience)Estimated Salary=10,737.30+2872.43(Education)+1129.1(Experience) Suppose an employee with 44 years of education has been with the company for 1111 years (note that education years are the number of years after 8th8th grade). According to this model, what is his estimated annual salary?
- The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of social science doctorates for each additional education doctorate.The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number…The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 120 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate.The slope tells us the decrease in the number of education doctorates for each additional social science doctorate. The slope tells us the increase in the number…A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…
- When is a variable in a regression statistically significant? 1 When p is more than alpha. 2 When p is more than R2. 3 When p is less than alpha. 4 When p is less than R2. 5 When p is less than the coefficient.If we collect monthly sales over two years for N=100 stores, we should not apply a simple linear regression model directly to the data, because the observations are not independent with each other. Is this statement True or False? A) True B) FalseIf the general linear regression model is given by the equation: y = a + b?; considering the informationobtained in Figure 2 above, compute the value of a.
