In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recenttransactions and estimates Price = 60 +6₁ Age + ε. A portion of the regression results is shown in the accompanying table. (You mayfind it useful to reference the t table.)StandardError732.41128.98InterceptAgea. Specify the competing hypotheses in order to determine whether the selling price of a used car and its age are linearly related.Coefficients21,268.91-1,201.23Ho: 612 0; HA: 61 < 0Ho: 61 = 0; HA: 61 0Ho: 61 ≤ 0; HA: 61 > 0Test statistict Stat29.040p-value1.42E-162.64E-08b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimalplaces.) c-1. Find the p-value.O p-value ≥ 0.10O 0.05 ≤ p-value < 0.10O 0.02 s p-value < 0.05O 0.01 ≤ p-value < 0.02O p-value < 0.01c-2. At the 5% significance level, is the age of a used car significant in explaining its selling price?weconclude that the age of a used car is significant in explaining its selling price.

a) Suppose β1 is the population slope coefficient of Age.

Answered: In order to examine the relationship…

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 4GP

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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?
In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates Price = Be + B1Age+ e. A portion of the regression results is shown in the accompanying table. Standard Error 734.41 p-Value 1.51E-16 2.02E-08 -1,203.251 126.91 a. Specify the competing hypotheses in order to determine whether the selling price of a used car and its age are linearly related. Intercept Age Coefficients 21,258.96 Test statistic 0; versus HA -9.481 t Stat 28.947 b. Calculate the value of the test statistic. Note: Negative value should be indicated by a minus sign. Round your answer to 3 decimal places. 10
Use the shoe print lengths and heights shown below to find the regression equation, letting shoe print lengths be the predictor (x) variable. Then find the best predicted height of a male who has a shoe print length of 28.5 cm. Would the result be helpful to police crime scene investigators in trying to describe the male? Use a significance level of α=0.05. Shoe Print (cm) 29.1 29.1 31.8 31.9 27.5 Foot Length (cm) 25.7 25.4 27.9 26.7 25.1 Height (cm) 175.4 177.8 185.2 175.4 173.2 The best predicted height is enter your response here cm. (Round to two decimal places as needed.) Would the result be helpful? A. No, because the description would be the same regardless of shoe print length. B. Yes, because the description would be based on an actual shoe print length. C. Yes, because the correlation is strong, so the predicted…
Conduct a hypothesis for whether consumption and income are linearly related using ? =0.01. The standard error of the slope is 0.144. Slope = 0.75, Intercept = 0, sample:Income 9, 11, 5, 8, 2, 9, 12Consumption 7, 7, 2, 7, 2, 8, 9 Step 1: State the null and alternative hypotheses.Step 2: Choose the significance level.Step 3: Calculate the test statistic.Step 4: Find the critical value(s).Step 5: Compare the test statistic to the critical value(s).Step 6: State the conclusion.
The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 640. The equation of the regression line is y= 34.756x + 16,820.956. Issues, x Proceeds, y 17,882 29,841 44,824 31,826|36,848 35,868 20,763 10,922 30,955 28,561 423 468 690 | 494 491 394 74 62 186 173 Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 640. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest million dollars as needed. Type your answer in standard form where "3.12 million" means 3,120,000.) O A. We can be 95% confident that when there are 640 issues, the proceeds will be between S and $ O B. There is a 95% chance that the predicted proceeds given 640 issues is between $ and $
A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age, X₂ = number of bankruptcies per 1.000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 50 people, calculate the calc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Predictor Intercept AgeMed Bankrupt FedSpend HSGrad% Answer is complete but not entirely correct. *calc 5.2526 -2.1764✔✔ 1.4101✔ Coefficient 4,198.5808 -27.3540 17.4893 -0.0124 -29.0314 SE 799.3395 12.5687 12.4033 0.0176 7.1268 -0.7045 -4.0736 p-value 0.0000 0.0348 0.2935 0.4848 0.0002
Listed 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 90 mm Hg. Use a significance level of 0.05 Right arm - 102; 101; 94; 79; 80 Left arm - 177; 172; 143; 144; 143 The regression equation is y(carety)= ___+___x. Given that the systolic blood pressure in the right arm is 90mm Hg, the best predicted systolic blood pressure in the left arm is _____ mm Hg.
Let's study the relationship between brand, camera resolution, and internal storage capacity on the price of smartphones. Use α = .05 to perform a regression analysis of the Smartphones01CS dataset, and then answer the following questions. When you copy and paste output from MegaStat to answer a question, remember to choose to "Keep Formatting" to paste the text. a. Did you find any evidence of multicollinearity and variance inflation among the predictors. Explain your answer using a VIF analysis. b. Copy and paste the normal probability plot for your analysis. Is there any evidence that the errors are not normally distributed? Explain. c. Copy and paste the Residuals vs. Predicted Y-values. Does the pattern support the null hypothesis of constant variance for the errors? Explain. d. Study the residuals analysis. Which observations, if any, have unusual residuals? e. Study the residuals analysis. Calculate the leverage statistic. Which observations, if any, are high leverage…
In a regression analysis, if SSE = 200 and SSR = 400, then the coefficient of determination is .67. .50. .40. .20.
The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. With the aim of predicting the used selling price from the number of miles driven, we might examine the least-squares regression line, y=41.57 – 0.49.x. This line is shown in the scatter plot in Figure 1. Used selling price, Mileage, x (in thousands) (in thousands of dollars) 25.9 26.1 28.1 26.2 40- 21.1 31.4 24.0 27.5 35 27.2 30.9 38.7 21.4 30. 34.6 25.5 37.2 23.5 15.6 34.0 25- 23.8 28.0 20.9 30.9 20. 23.1 32.7 28.0 30.3 40 29.2 28.1 Figure 1 24.0 29.6 23.0 31.5 Send data to Excel
Use the summary statistics to calculate the regression line for this data. Explain each coefficient. What is the total amount of weight would you expect a weightlifter with a body weight of 84kg to lift? At the 5% significance level, is there evidence that the body weight of the athlete is a useful predictor for the total amount an athlete can lift? Assume the assumptions can be verified.

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