We want to estimate the effect of x on y using a simple linear regression. Assume that the MLR 1-6 hold and the true effect of x is zero. What is the probability that the t-statistic of the slope coefficient in the above regression is positive? а. 95% b. +/- 1.96 O C. 5% O d. 50%
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- Suppose that you run a correlation and find the correlation coefficient is -0.281 and the regression equation is y = 27.68 2.2x. The mean for the data values was 4.9, and the mean for the Y data values was 17. AT Test for the slope of the regression line is performed, and the p-value is greater than the level of significance of 0.05. Use the appropriate method to predict the y value when x is 2.3.What is the value of r2? Use the square root and your knowledge about the slope of the regression line to find the value of the correlation constant r. Based only on the value of r, do you think this line is useful for predicting life expectancy from the infant mortality rate? A new country called Arendelle has formed and has an infant mortality rate of 42 (deaths per 1000 live births). Use the equation of the regression line to predict the life expectancy for Arendelle. Round your answer to one decimal place. Another new country called Weselton has formed and has an infant mortality rate of 250 (deaths per 1000 live births). Recall some of the cautions we should take when considering correlation. In one or two complete sentences, explain why using the linear regression equation to make a life expectancy prediction is not a good idea for Weselton. If you had to choose exactly one potential influential outlier from the original data set, what would it be? Identify the point as an…If a correlation isr= 0.00, then SP = 0 and the regression equation is O Ý =X +0 O Ý =X + X O Ý =0 + X O Ý =Ÿ + 0
- If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. Select one: True FalseThe coefficient of correlation in a simple regression analysis is = -0.6. The coefficient of determination for this regression would be 0.36 - 0.36 0.6 0.13 O 0.6 or + 0.6Identify the correct statement concerning, r the correlation coefficie between X and Y and the linear regression, Y = aX+b. A. Both can be used to show cause and effect. B. Both quantify the strength of relationship between X and Y. C. X and Y are interchangeable in both relationships. D. Both can be used to make predictions.
- We collected teacher ratings for 25 courses taught by an instructor over a six-vear period. The students' ratings of the instructor are on a scale of 1 to 9. We found that The linear regression equation is: Average Rating = 7,88 -0.068 Numher of Students 1. Interpret the slope of this model including units: The average rating decreases per each additional student 0.068 ed teacher rating for a class size of 15 students using the given 7.88 prediction equation is Next page CS Scanned with CamScannerIf the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. True or false?A researcher would like to predici the dependent variable Y fram the two independent variables X, and Xg for a sample of N = 18 subjecis. Use muliple linear regression to calculate the coefficient of multiple determination and Lest the significance of the overall regression model. Use a significance level a = 0.01. Y 53.2 42.4 56.6 75 32.2 62.9 68.2 26.9 70.1 63 30.9 57,4 52 44.2 70.1 52.9 33 55.9 67.8 35.3 54.9 51.1 49 47.8 39.5 57.4| 46.9 45.7| 52.7 60.5 57.2 43.2 61.1 40.4 42 | 45,7 56.1 42.2 37.3 51.8 | 58.9 53,4 51.9 42.2 47.5 37.1 48 46.8 66 33.8 | 61.7 32.3 53.4 57.5 F= Pvalue - What is your decision for the hypothesis test? O Reject the null hypothesis, H.:B, = B =0 O Fail to reject H, What is your final conclusion? O The evidence supports the claim that one ar more of the regression coefficients is non-zero O The evidence supports the claim that all of the regression coelfficients are zero OThere is insufficient evidence to support the claim that at least one of the regression…
- The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year periods are shown in the table. The equation of the regression line is y = 0.942x +27.609. Find the standard error of estimate s, and interpret the result. 793.9 1042.3 957.7 1203.3 450.7 673.7 745.1 778.6 Money raised, x Money spent, y 734.8 1024.2 929.1 1160.6 448.6 697.9 735.7 751.2 Find the standard error of estimate s, and interpret the result. (Round to three decimal places as needed.) How can the standard error of estimate be interpreted? O A. The standard error of estimate of the money raised for a specific amount of money spent is about s, million dollars. O B. The standard error of estimate of the money spent for a specific amount of money raised is about s, million dollars.A set of n = 15 pairs of X and Y scores has SSX = 10, SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X? a. 10/30 b. 10/40 c. 40/10 d. 30/10Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 90 mm Hg. Use a significance level of 0.05. Right Arm 101 100 92 77 77 Left Arm 174 169 145 146 146
