Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = X + y 1 30.12 2 30.98 3 26.34 4 23.8 5 25.46 6 20.02 7 19.68 8 17.64 9 17.7 10 16.26 11 14.32 12 11.88 13 9.94 14 6.8 X 777306
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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 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.Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 5 8.3 6 9.06 7 9.12 8 11.98 9 8.44 10 12.4 11 9.56 12 11.22 13 10.08 14 10.74
- A marketing manager conducted a study to determine the relationship between money spent on advertising (X) and company sales (Y). The study consisted of 8 companies and the data is given below and is in units of $1000s (ie. 2.4 = $2400.00) d. What is the resulting residual value when advertising expenditure is $2200.00 (X = 2.2), that is the difference between the actual observed value of y and the predicted value of y when using the fitted regression equation? e. What percentage of the variation in company sales is explained by the regression equation? In other words, what is the variability in Y that is due to advertising? Does a…Use the given data to find the scatterplot, equation of the regression line, and prediction. x 1.2 1.4 1.6 1.8 2.0 y 54 53 55 54 56 Let α=0.05 Scatterplot from the calculator: What is the linear regression equation? (Round to 3 decimal places) ^ y= _________________________________________________________________ r = _______________ critical value from table: ________________ Is there a strong enough linear correlation to use the regression equation given? ___________ Explain why? _____________________________________________________ What is the best predicted y-value when x=1.9 ? _______________A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The regression equation is given below, where x denotes seed density, and y denotes lawn quality. The correlation coefficient r = .600. y = 33.14 + 4.54x If possible, use the information to obtain an estimate of the mean lawn quality for all lawns sown with a seed density of 4.7 (assume 4.7 is within the domain of the observed seed densities). Pay attention to all details before choosing your answer of the 4 below. Choices: A.) Since the correlation coefficient, r, is less than rcrit = 0.707, the correlation is significant and the lawn quality estimate is 54.48. B.) Since the correlation coefficient, r, is less than rcrit =…
- Annual high temperatures in a certain location have been tracked for several years. Let XX represent the year and YY the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 2 4.13 3 1.72 4 4.21 5 1.9 6 4.69 7 1.68 8 2.27 9 1.86 10 2.25 11 3.14 12 1.53 13 0.72 14 0.51 15 3.5Which 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 aboveThe height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Stories Height (in feet) 57 1050 28 428 26 362 40 529 60 790 22 401 38 380 110 1454 100 1127 46 700 b. What is your regression line written in the form ŷ = a + bx? (Round a and b to 3 decimal places please!) ŷ = _____ + ______ x b. Use your regression equation above to predict the height of a building with 7070 stories: ________ (Please enter a whole number) c. Compute the coefficient of determination (write it as a decimal here). ___ d. Determine the percentage of the variation in the observed values of the response variable, height, explained by the regression with the explanatory variable, stories. _________%
- A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90, R2 = 0.67; DW = 2.08 How would you interpret the above ‘Output’ of a regression analysis performed in SPSS?Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance Attitute59 7263 6765 7869 8258 7577 8776 9269 8370 8764 78 A. y=11.7+1.02x B. y=2.81+1.35x C. y=−47.3+2.02x D. y=92.3−0.669xAn article reported that for a regression of y = average SAT score on x = expenditure per pupil, based on data from n = 44 New Jersey school districts, a = 766, b = 0.015, r2 = 0.160, and se = 53.7. One observation in the sample was (9400, 897). What average SAT score would you predict for this district, and what is the corresponding residual?Predict average SAT score _______ Residual ________