11.21 Consider the following pairs of measurements. D L11021 x y 54 5 4 33 3 -1 2 7 3 0 1 8 65 5 43 3 a. Construct a scatterplot of these data. b. What does the scatterplot suggest about the relation- ship between x and y? xx c. Given that SS = 43.4286, SSxy = 39.8571, y = 3.4286, and 3.7143, calculate the least squares estimates of Bo and B. 020; .918 d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain. e. Interpret the y-intercept and slope of the least squares line. Over what range of x are these interpretations meaningful?
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- L11046 X y 11.46 Consider the following pairs of observations: 1 1 4 3 3 3 2 1 5 4 6 7 0 2 a. Construct a scatterplot for the data. b. Use the method of least squares to fit a straight line to the seven data points in the table. c. Plot the least squares line on your scatterplot of part a. d. Specify the null and alternative hypotheses you would use to test whether the data provide sufficient evidence to indicate that x contributes information for the (linear) prediction of y. e. What is the test statistic that should be used in conducting the hypothesis test of part d? Specify the degrees of freedom associated with the test statistic. f. Conduct the hypothesis test of part d using a = = .05.11.13 please do it in steps because i don't knowA simple linear regression was performed on 25 observations. The least squares calculations are given as: SSxy = 204, SSxx= 100, SSyy = 516. Calculate SSE. O 99.84 O 4.34 O 516 O 2.04
- The following data represent the commute time (in minutes) x and a score on a well-being survey y. The equation of the least-squares regression line is y=-0.0468x + 68.9967 and the standard error of the estimate is 0.5157. Complete parts (a) through (e) below. X 5 T y 69.0 Lower Bound Upper Bound 15 25 35 50 72 105 68.2 67.4 67.1 66.8 66.5 63.6 (a) Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes. y= (Round to two decimal places as needed.) (b) Construct a 90% confidence interval for the mean well-being index composite score of all individuals whose commute time is 20 minutes. = (Round to two decimal places as needed.) = (Round to two decimal places as needed.) G (c) Predict the well-being index composite score of Jane, whose commute time is 20 minutes. y= (Round to two decimal places as needed.) (d) Construct a 90% prediction interval for the well-being index composite score of Jane, whose commute time is 20 minutes. Lower Bound…Please answer 4.13Given are five observations for two variables, and y. The estimated regression equation for these data is = 75.74-2.92x. a. Compute SSE, SST, and SSR. Yi The least squares line provided an - Select your answer decimal). fit; 4 SSE (to 2 decimals) SST (to 2 decimals) SSR (to 2 decimals) b. Compute the coefficient of determination ². Comment on the goodness of fit. (to 3 decimals) 00 15 18 20 57 57 46 17 12 Check My Work (2 remaining) % of the variability in y has been explained by the estimated regression equation (to 1 c. Compute the sample correlation coefficient. Enter negative value as negative number. (to 3 decimals)
- 2.60. Show that test statistics (2.17) and (2.87) are equivalent. Since (b₁-B₁)/s(b) is distributed as t with n - 2 degrees of freedom, tests concerning B₁ can be set up in ordinary fashion using the distribution. Two-Sided Test A cost analyst in the Toluca Company is interested in testing, using regression model (2.1), whether or not there is a linear association between work hours and lot size, i.e., whether or not B₁ = 0. The two alternatives then are: Ho: B₁ = 0 (2.16) He: B₁ 0 The analyst wishes to control the risk of a Type I error at a = .05. The conclusion H, could be reached at once by referring to the 95 percent confidence interval for , constructed earlier, since this interval does not include 0. An explicit test of the alternatives (2.16) is based on the test statistic: b₁ (2.17) s(b₁) The decision rule with this test statistic for controlling the level of significance at a is: (2.18) If t ≤t(1-a/2;n -2), conclude Ho t(1-a/2;n-2), conclude Ha If Ir Point Estimator of P12.…2. Find the quartiles for these data values: 5, 7, 7, 8, 10, 11, 12, 15, 17 OAQ₁ 7.Q₂ Q2 OB. Q₁ 7.Q₂ = 10.Q3 - 13.5 = Oc. Q₁ = 6, Q2 = 9, Q3 = 12 OD. Q₁ 7.5. Q₂ [Am] ( = 11. Q3 = 15 10.5 Q3 = 13.5Table 14.17 The Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05? Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01? Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model? Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval. Calculate the 99 percent confidence interval for…
- The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface? Use α=0.01. Weight, x 5930 5390 6500 5100 5890 4800 Variability in braking distance, y 1.76 1.95 1.91 1.62 1.64 1.50 1.Setup the hypothesis for the test. Choose a or b H0: ρ ▼ A.less than or equals≤ b.less than< c.equals= d.greater than> e.greater than or equals≥ f.not equals≠ 0 Ha: ρ ▼ A. less than or equals≤ b.less than< c.equals= d.greater than> e.greater than or equals≥ f.not equals≠ 0 2.Identify the critical value(s). Select the correct choice below and fill in any answer boxes within your choice. (Round to three decimal places as needed.) Fill the correct answer A. The critical value is= B. The critical…A spectrometer was used to measure the light absorbed by three standard solutions containing different concentrations of K2Cr207. The following data was obtained. Absorbance 0.162 0.320 [C] (ppm) 5.1 10.0 14.9 0.486 The equation of the straight line generated using the method of least squares is: y = 0.0331x - 0.0086. Use this information to find the standard deviation of the slope of the line expressed to the proper number of significant figures. O a. m = 0.0331 (±0.0045) b. m = 0.033 (±0.004) Oc. m = 0.0331 (±0.0001) d. m = 0.0331 (+0.0101)Do males make significantly more money than females at RIT? Be sure to weight the variables in SPSS Ver.29. Interpret all results. Gender Salaries Weight Male $88,000 15 Male $99,000 16 Male $80,000 10 Male $90,000 10 Male $99,999 12 Male $79,000 11 Female $50,000 10 Female $62,000 15 Female $55,000 10 Female $45,000 10 Female $24,000 15 (I need a output from SPSS; and Interpretion)If you are unable to provide the output from SPSS then please provide the instructions step-by-step on how I can get the text output.