Which statement is true about the data shown below (a=0.05) 20 40 60 80 y 24 1.20 1.71 2.22 a. The regression line doesn't pass through the origin b. R2=0.9716 c. There is no linear relationship between y and x O Od. Y= 0.270+ 0.03225 X
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- 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?Use the sample linear regression line Y^=2+3X for the data points below to answer the following questions. X 0 3 7 10 Y 5 5 27 31 1) What is the fitted value when X2=3? 2) What is the regression residual when X2=3?
- The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433xThe marketing manager of a supermarket chain would like to determine the effect of shelf spaceon the sales of pet food. A random sample of 10 stores was selected, and the results are presentedbelow. Store shelf space in cm weekly sales in thousand pesos 1 45 18 2 45 21 3 75 15 4 80 18 5 95 23 6 100 26 7 135 22 8 140 27 9 185 25 10 190 28 d. Using the estimated simple linear regression equation Y=15.6414+0.0611X, estimate the weekly sales when theshelf space is 230cm? 250cm? e. Compute the coefficient of determination and interpret its value.
- Consider the following table of N=3 observations. Calculate estimates of b1 and b0 (b-hat) considering the linear regression model y=b+b*x Compute SSE for this regression Assume that SST=32. What is R^2 for this regression?Which of the following expressions is the correct way to express an interpretation for an OLS regression coefficient of -0.9? - This question is based on Data Analysis A. For every one unit increase in X there is - on average - a 0.9 unit decrease in Y. B. For every one unit increase in Y there is - on average - a 0.9 unit decrease in X. C. For every one unit increase in Y there is - on average - a 0.9 unit increase in X. D. For every one unit increase in X there is - on average - a 0.9 unit increase in Y.Which of the following best describes a regression coefficient in a bivariate setting? a. The change in Y predicted by a unit change in X b. The slope of a line that minimizes the sum of squared residuals c. The correlation coefficient multiplied by SDy/SDx d. All of the above
- The following multiple regression printout can be used to predict a person's average annual salary given his or her years of employment and number of years of education beyond high school. Regression Analysis: Salary Versus YrsEm, Educ Coefficients Term Coef SE Coef T-Value P-Value Constant 23,175 1,771 13.09 0.000 YrsEm 671 141 4.76 0.000 Educ 1,911 378 5.06 0.000 (a) Is the regression coefficient of education (Educ) statistically significant? (Use ? = 0.05.) Given this output, the regression coefficient for education (is/is not) statistically significant. (b) Does the variable education belong in the model? Given this output, the variable education (may/may not) belong in the model. (c) Given this output, which of the following is the correct interpretation for Education in this model? -For each additional year of education beyond high school, the estimated change in the average annual salary is $23,175, controlling for years of employment. -For each…Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x 7 4 12 3 6 10 8 13 11 5 9 y 14.61 7.56 18.76 4.45 12.64 18.24 16.21 18.45 18.70 10.30 17.41 y^=???+1.41.4x (Round to two decimal places as needed.)Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 11 21 34 36 39 36 Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to one decimal place and b1 to two decimal places and b2 to four decimal places.) ŷ = (e) Use the results from part (d) to test for a significant relationship between x, x2, and y. Use ? = 0.05. Is the relationship between x, x2, and y significant? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = (f) Use the model from part (d) to predict the value of y when x = 25. (Round your answer to three decimal places.)