Concept explainers
Testing Hypotheses About Regression Coefficients If the coefficient β1, has a nonzero value, then it is helpful in predicting the value of the response variable. If β1 = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that β1 = 0 use the test statistic t = (b1 − 0)/
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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?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_forwardLife Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. 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 as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forward
- What is regression analysis? Describe the process of performing regression analysis on a graphing utility.arrow_forwardA Bivariate Regression was conducted to evaluate the predictive relationship between total years of schooling and annual income. The results of the regression model were F(1,88) = 4.1, p < .05. What can be concluded about these results? Group of answer choices total years of schooling is a significant predictor of annual income. total years of schooling is not a significant predictor of annual income.arrow_forwardObservations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars). X₁ = display floor space (square meters), X₂= competitors' advertising expenditures (thousands of dollars), X₁ = advertised price (dollars per unit). Predictor Intercept FloorSpace CompetingAds Price Coefficient 1,243.88 13.74 -6.848 -0.1461 (a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) *FloorSpace+ *CompetingAds+ (b-1) The coefficient of FloorSpace says that each additional square foot of floor space O takes away 13.74 from sales (in thousands of dollars) O adds about 13.74 to sales (in thousands of dollars) adds about 6.848 to sales (in thousands of dollars) takes away 01496 from sales (in thousands of dollars) (b-2) The coefficient of CompetingAds…arrow_forward
- COmpare and constrast the use of prediction intervals for a Single Linear Regression model having one X and Multiple Linear Regression Model having two predictors X1 and X2. WHat are the similarities/differences in process and interpretation?arrow_forwardWhat is the difference between a Multiple Regression model and a Multivariate Regression model? Suppose a researcher wants to predict the probability of a patient being diagnosed with breast cancer given their be used? age, family history, and smoking status. What type of regression model should alsboin sisiurviluM bae alqiluM alm?arrow_forwardBivariate data obtained for the paired variablesx and y are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y =-4.87+1.06x . In the "Calculations" tabl : calculations involving the observed y values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 團 160+ 6-7 G-7) G- х 150+ 111.4 115.6 318.9796 409.9005 5.6930 140 122.2 121.5 143.0416 77.4048 9.9982 132.0 139.8 40.1956 2.5281 22.5625 130+ 138.6 130.1 11.2896 73.7194 142.7069 120- 151.1 160.3 720.3856 476.8109 25.0400 110- Column 1233.8920 1040.3637 206.0007 sums 110 120 130 140 150 160 Send data to Excel Figure 1 Answer the following: 1. The variation in the sample y values that is not explained by the estimated linear relationship between x and y is given by the ? v, which for these data is ? 2. The value r is the…arrow_forward
- please show work on a piece of paperarrow_forwardIn multiple regression analysis, explain why the typical hypothesis that analysts want to test is whether a particular regression coefficient (B) is equal to zero (H0: B = 0) versus whether that coefficient is not equal to zeroarrow_forwardUse appropriate statistical tables when necessary. What is the dependent and independent variables? Fully write out the regression equation. Fill in the missing values * and **. Test whether ᵟ is significant and give reasons for your answer.arrow_forward
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