Compute the least-squares regression line for predicting y from x given the following summary statistics. Round the slope and y- intercept to at least four decimal places. x= 8.2 S- 2.2 y= 30.2 = 103 r=0.40 Send data to Excel Regression line equation: y =
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- Critical Values of the Pearson Correlation Coefficientr a= 0.05 a= 0.01 NOTE: To test H, p-0 against H,: p#0, reject H, jr the absolute value of r is preater than the critical yalue in the table. 0.950 0.990 0.959 0.917 0.875 5 0.878 6 0.811 0.754 7 0.834 0.798 8 0.707 0.666 0.632 0.602 9 10 0.765 11 0.735 12 0.576 0.708 13 0.553 0.684 0.532 0.514 0.497 0.482 14 0.661 15 0.641 16 0.623 17 18 0.606 0.590 0.468 19 0.456 0.444 0.575 20 0.561 25 0.396 0.505 0.463 30 0.361 35 0.335 0.430 40 0.312 0.402 45 0.294 0.279 0.378 0.361 50 60 0.254 0.330 70 80 0.236 0.305 0.286 0.220 90 0.207 0.196 0.269 100 0.256 a= 0.05 a=0.01Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is Price = B + OBedroom + yHouse Size + ALot Size Coef SE Coef Predictor T Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 0.164 Lot Size -4.36 17.02 -0.26 0.798 R-Sq=56.0% R-Sq (adj)=54.6% S= 25023 Source DF MS F P Regression 3 76501718347 25500572782 *** **** Residual Error 96 60109046053 626135896 Total 99 a) Write out the regression equation. b) Fill in the missing values *, **, c) Use the p-value approach to determine if ø is significant at the 5% significance level and d) Is y significantly different from -0.5? e) Perform the F test at the 1% level, making sure to state the null and alternative hypotheses. f) Give an interpretation to the term "R-sq" and comment…The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x= 5 wins E Click the icon to view the table of numbers of wins and earned run average. (b) x = 10 wins (c) x = 19 wins (d) x= 15 wins ..... The equation of the regression line is y = x+O (Round to two decimal places as needed.) Wins and ERA Earned run Wins, x average, y 20 2.71 18 3.19 17 2.69 16 3.68 14 3.94 12 4.25 11 3.86 9 5.18 Print Done
- Use the time/tip data from the table below, which includes data from New York City taxi rides. (The distances are in miles, the times are in minutes, the fares are in dollars, and the tips are in dollars.) Find the regression equation, letting time be the predictor (x) variable. Find the best predicted tip for a ride that takes 30 minutes. How does the result compare to the actual tip amount of $4.70? Use a significance level of 0.05. Distance 1.80 12.71 1.32 Time 1.65 8.51 1.40 1.02 2.47 Fare Tip 25.00 27.00 8.00 16.30 36.80 7.80 9.80 31.75 12.30 1.50 0.00 0.00 1.96 2.98 2.46 11.00 31.00 18.00 8.00 18.00 7.80 14.30 2.34 4.29 The regression equation is ŷ =+ (x. (Round the y-intercept to two decimal places as needed. Round the slope to four decimal places as needed.)The local utility company surveys 12 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis is as follows: bill = 16.2 + 3.58. size. Coefficients Estimate Std. Error (Intercept) 16.2 Size 3.58 0.47 0.68 Round your answer to three decimal places, and round any interim calculations to four decimal places. We are 99% confident that the mean annual electric bill increases by between dollars for every additional square foot in home size. dollars andThe data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 58 inches. Is the result close to the actual weight of 572 pounds? Use a significance level of 0.05. Chest size (inches) 46 57 53 41 40 40 Weight (pounds) 384 580 542 358 306 320 LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? y=nothing+nothingx (Round to one decimal place as needed.)
- Researchers are interested in predicting the height of a child based on the heights of their mother and father. Data were collected, which included height of the child ( height), height of the mother ( mothersheight ), and height of the father (fathersheight ). The initial analysis used the heights of the parents to predict the height of the child (all units are inches). The results of the analysis, a multiple regression, are presented below. . regress height mothersheight fathersheight Source Model Residual Total height mothersheight fathersheight _cons SS 208.008457 314.295372 522.303829 df 2 104.004228 8.49446952 37 MS 39 13.3924059 Coef. Std. Err. .6579529 .1474763 .2003584 .1382237 9.804327 12.39987 t P>|t| 4.46 0.000 C 0.156 0.79 0.434 Number of obs = F( 2, 37) = Prob > F R-squared Adj R-squared = Root MSE = = .3591375 -.0797093 -15.32021 = 40 12.24 0.0001 0.3983 0.3657 2.9145 [95% Conf. Interval] .9567683 .4804261 34.92886 What are the null and alternative hypotheses…The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x = 5 wins Click the icon to view the table of numbers of wins and earned run average. (b) x = 10 wins (c) x = 21 wins (d) x = 15 wins ERA 6- ERA 6- AERA 6- ERA 6- 4- 4- 4- 4- 2- 2- 2- 2- 0+ 6 0- 0- 0- 12 18 24 6. 12 18 24 12 18 24 6 12 18 24 Wins Wins Wins Wins (a) Predict the ERA for 5 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. ŷ= (Round to two decimal places as needed.) B. It is not meaningful to predict this value of y because…The following table gives the data for the grades on the midterm exam and the grades on the final exam. Determine the equation of the regression line, y = bo + b₁x. Round the slope and y-intercept to the nearest thousandth. Grades on Midterm and Final Exams Grades on Midterm 78 70 84 97 82 75 75 88 67 76 89 79 88 100 Grades on Final 71 80 77 77 72 65
- The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y = 1.405x – 12.307. Complete parts (a) and (b) below. Average Weekly Wages (state), x Average Weekly Wages (federal), y 751 760 791 817 835 881 924 951 1002 1047 1115 1149 1195 1250 1269 1300 (a) Find the coefficient of determination and interpret the result. 12 =OListed 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 85 mm Hg. Use a significance level of 0.05 Right Arm 101 100 94 75 Left Arm 174 167 146 144 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is (Round to one decimal place as needed.) 76 144 CRITS
