The temperatures (Observed and Expected) in centigrade forcertain concrete mix sample have been presented as shown in thetable below:ObservedExpectedFrequencyFrequency91019212725292720241621810a- Use the data above to determine the Correlation Coefficient, betweenthe Expected and the Observed frequenciesb- Use the data above to determine the equation of the regression linebetween the expected and the observed frequencies.Note: Let the Observed values represent X and the Expected values represent Y.

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Answered: The temperatures (Observed and…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4PPS

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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?
4. For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 3388, Σγ^2 = 57365692 a) compute correlation coefficient (b) Find the fitted regression line of the price of laptop on processor speed.
The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x�^=�0+�1�. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.050.05 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉℉) 3939 2525 1515 4242 4242 2424 3232 2020 3030 3737 Snow Accumulation (in.in.) 66 1515 2929 66 1414 2626 2323 1212 1616 77 Copy Data Regression equation: yˆ=�^= Is the equation appropriate? Yes
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1xy^=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.01 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉℉) 42 27 22 39 44 21 27 18 32 36 Snow Accumulation (in.in.) 6 11 22 8 12 27 27 20 12 6 Regression equation y=_______________ Is the equation appropriate?
A study of the amount of rainfall and the quantity of air pollution removed produced the following data shown in table below: Daily Rainfall x (0.01 cm) Particulate Removed y (μg/m3) 7 126 7.9 129.3 7.5 125.3 9.2 120.2 10.8 116.7 5.8 119.2 5.6 138.7 2.7 147.5 9.2 110.3 Compute and interpret the coefficient of determination, and coefficient of correlation for the given data. What will be the regression equation, when swapped depended and independent variable
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.01 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉) 42 27 22 39 44 21 27 18 32 36 Snow Accumulation (in.) 6 11 22 8 12 27 27 20 12 6
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1xy^=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.01 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperatures and Snow Accumulations Average Temperature (℉℉) 45 31 16 35 35 22 26 23 25 39 Snow Accumulation (in.in.) 9 20 23 6 10 29 22 14 12 9 Question 1: Regression equation y=__________ Question 2: Is the equation appropriate? Yes or No?
4.For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 33.88, Σγ^2 = 57365692 (b)Find the fitted regression line of the price of laptop on processor speed. (c) Find the predicted price of the laptop (y) for the processor speed x-1.9. (d) Compute the coefficient of determination and comment.
The following is a partial computer output of a multiple regression analysis of a data set containing 20 sets of observations on the dependent variableThe regression equation isSALEPRIC = 1470 + 0.814 LANDVAL + 0.820 IMPROVAL + 13.5 AREA Predictor Coef SE Coef T P Constant 1470 5746 0.26 0.801 LANDVAL 0.8145 0.5122 1.59 0.131 IMPROVAL 0.8204 0.2112 3.88 0.0001 AREA 13.529 6.586 2.05 0.057 S = 79190.48 R-Sq = 89.7% R-Sq(adj) = 87.8% Analysis of Variance Source DF SS MS Regression 3 8779676741 2926558914 Residual Error 16 1003491259 62718204 Total 19 9783168000 For the problem above, we want to carry out the significance test about the coefficient of LANDVAL, what is the t-value for this test, and is it significant? 46.66, significant 2.05, significant 1.59, not significant 0.26, not significant
Interpret the estimated regression coefficient corresponding to the Z variable. Data Salary Education Experience Sex 29.7985 15 3 1 21.8219 4 0 0 22.8978 4 0 0 22.0917 1 1 0 21.8993 5 0 0 22.4829 3 1 1 28.0772 15 0 0 y=salary 23.6292 6 1 1 x1=education level in schooling years 32.3595 0 15 1 x2=experience level in employment level 21.794 1 0 0 d=sex (1 for male,0 for female) 19.8762 3 0 0 Ln(Y) = alpha +beta1X1 +Beta2X2+ Beta3D +Beta4Z +e 21.0253 3 0 0 where z =X2D 24.6323 0 5 1 19.0247 0 0 0 18.8857 0 0 0 21.8552 1 0 0 24.2675 6 1 0 18.7931 0 0 0 18.9276 0 0 0 23.4441 5 1 1 20.8047 2 0 0 18.26 0 0 0 20.6726 0 2 1 21.7815 3 0 0…
A sample of 40 individuals collects their shoe size and the height (cm) for CSI data. The scatter plot and results from a simple linear regression are recorded: HEIGHT = 126.76238 + 4.8782178 SHOE SIZE Sample size: 40R (correlation coefficient) = 0.77918855P-value < 0.0001 (a) Does the scatterplot and results show a linear correlation between shoe size and height? (b) How can you tell? (c) Will it be appropriate to use the linear regression equation given in the output? (d) Krusty the Clown wears size 8.5 shoes. According to the linear regression equation, how tall is Krusty the Clown? (e) Sideshow Bob wears size 14 shoes. According to the linear regression equation, how tall is Sideshow Bob?

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