F(a) = (z, - a)? (7) i=1 is minimal when a = . (As a consequence, the sample mean is also called the least squares estimator of the population mean.)
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- (a) The correlation coefficient: r = (b) The least squares line: ỹ = %3DA study of IT companies has found the following data on the age of each company and its annual volume of sales: Age (years) Sales (000) 2 22 2.5 34 3 33 4 37 4.5 40 4.5 45 5 49 3 30 6 58 6.5 58 (a) Determine the least squares regression that relates the age of company variable to the sales variable in the form y = a + bx. (b) Provide a practical interpretation of the coefficients a and b. (c) Determine the ‘goodness of fit’ (R2) of the estimated regression line. d) Using the estimated regression line determined in (a), calculate what volume of sales would be predicted for a company that is 3.5 years of age. (e) If it was found that…A statistician wishes to examine the relationship between average monthly rainfall (in mm), x, and number of road accidents, y, in a particular city. The following calculations have been done for you: Ex = 276, Ex2 = 6888, Ey = 193, Ey 3421, Exy 4842 and n 12. !3! The equation of the least squares regression line is given by
- Are MRI count and IQ linearly related? Because the correlation coefficient for females is negative/positiveand the absolute value of this correlation coefficient, enter your response here#, is greater/not greater than enter your response here#, the critical value for the female data set,no/a positive/a negativerelation exists between MRI count and IQ for females. Because the correlation coefficient for males is negative/positive and the absolute value of this correlation coefficient, enter your response here#, is greater/not greater than the critical value for the male data set, enter your response here#,no/a positive/a negative relation exists between MRI count and IQ for males. (Round to three decimal places as needed.) Critical value table 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374…A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[1] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and O otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender Because Female is a dummy variable, the problem provides us with enough information to figure out the exact regression line equation. What is the numerical value of a?A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
- The null hypothesis being tested in the least-squares regression output for B is B1 = B1,0=1. True FalseExample 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 8 8. 10 4 7 Marks in 2nd Test (Y) 8 7 7. 10 5 8. 10 6. (a) Find the least square regression line of Y on X. / 7,A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y; = -13258.594 + 2.422X;, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000- 20000 0. -20000 -20000 a) To evaluate whether the assumption of linearity has been violated, which of the following graph shou be examined? A. Predicted Values vs. Residuals B. Residual index plot C. QQ plot of residuals D. Residuals vs. Progrm Per-Year Tuition ($) b) To evaluate whether the assumption of normality has been violated, which of the following graph…
- The least-squares line for predicting forearm length (y) from height (x) is y = -0.2967 + 0.2738x How tall must a man be so that we would predict his forearm length to be 19.4 in.? a. 69.77 b. 70.85 c. 65.39 d. 71.94 e. 73.15Absences and Final Exam Scores No. of absences, x 0 1 For students WHO IIISS THO Classes is et the slope or the y-intercept. = as needed.) Final exam score, y 88.9 86.6 83.6 81.5 student who misses five class periods. 2 Print 3 = needed.) ow average for this number of absences? 4 5 78.2 73.7 Done 6 7 8 63.9 72.7 It is not appropriate to interpret the slope. 9 65.3 65.4 0 O X Reference 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.997 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.
