The table gives the readings from a laboratory experiment 3 6. 9. 17 49 71 161 A curve of the form y= ea(E-b)to the above data by method of discrete least squares approximation
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experiment
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3
9
17
49
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A curve of the form y= ea(t-b)to the above data by
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- The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area x (in hectares). X 6² Round your intermediate answers to four decimal places (e.g. 98.7654). (a) Fit the simple linear regression model using the method of least squares. Find the estimate of ². Round your answer to the nearest integer (e.g. 9876). i B₁ = (b) What change in the mean mass is expected when the field area changes by 1 hectare? Round your answer to the nearest integer (e.g. 9876). ŷ: 7280 15730 13590 19820 12860 = 2.01 3.93 3.68 4.33 2.33 (c) Calculate the fitted value of y corresponding to x = 2.01. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). =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 byThe heights (y) and lengths of forearms (x) were measured in inches for a sample of men. The following summary statistics were obtained: x= 10.1 Sx=0.8 y= 70.1 Sy=2.5 r=0.81 a. Compute the least- squares regresson line for predicting height from forearm length. b. Joe's forearm is 1 inch longer than Sam's. How much taller than Sam do you predict Joe to be? c. Predict the height of a man whose forearm is 9.5 inches long.
- The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.6667, sx =2.4221, y = 3.8667, sy = 1.8435, andr= -0.9525, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). D O A. (a) Choose the correct graph below. Ay 6- X y 0 0 2 3 5 6 6 5.8 5.7 5.0 2.8 1.7 2.2 O G B. Ay 6- Q (...) C. 0- ● Q D. Ау 0- X 62 3 3 3 0 -1 1 8.0 L11021 8. y a. Construct a scatterplot of these data. b. What does the scatterplot suggest about the relation- ship between x and y? c. Given that SSxx = 3.4286, 43.4286, SSy = 39.8571, ỹ and x = 3.7143, calculate the least squares estimates of %3D %3D ху %3D %3D Bo and B1. d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain. on the plot. e. Interpret the y-intercept and slope of the least squares line. Over what range of x are these interpretations meaningful? 14 65
- The table gives the readings from a laboratory experiment 2 3. 3. 15 b+x A curve of the form y= to the above data by a+x method of discrete least squares approximationConsider the following pairs of measurements: a. Use Stata to chart a scattergram for the data. Show the graph below. X 5 8 3 4 9 Y 6.2 3.4 7.5 8.1 3.2 b. Use Stata to estimate the least squares model between X and Y. Copy the output below and specify the least squares equation. c. What are SSE, s2, and s?The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Constant Weight S = 0.517508 Coef 0.8462 0.39512 R-Sq 97.0% (a) Write out the least-squares equation. ŷ = = 0.8462 + 0.39512 X SE Coef 0.4148 0.02978 T 2.06 13.52 P (c) What is the value of the correlation coefficient r? (Use 3 decimal places.) X 0.84 0.000 (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.) 0.39512
- A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x=3.8333, sx=2.4014, y=3.6500, sy=1.7942, and r=−0.9539, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a).If beta1_hat = 0.4571 use the data below to find beta0_hat for the simple linear model using the method of Least Squares. Y 17 2 3 11 4 20 15 18 13 13.07 50.88 24.57 32.11A researcher wishes to investigate the association between two variables, denoted xi and yi. The following results have been obtained from the analysis of a sample of 30 observations: Sxi = 119.2, Syi = 129.2, Sxi yi = 480.9, xSi2 = 493.6 (xi −x)2 = 20.4, ei2 =444.2 Calculate the ordinary least squares (OLS) estimates of the coefficients of the linear regression, yi = β1 + β2xi +ui. What does your estimate of β2 in part (i) suggest about the association between xi and yi. Calculate the standard error of the regression, ˆ , and the standard error of the estimated slope coefficient, se(ˆ2) . Test the null hypothesis H0: 2=0 against the alternative hypothesis H1: 20, using a significance level of 0.05. On the basis of your hypothesis test in part (iv), is there any evidence of an association between xi and yi?
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