Find the independent nonlinearity and the correlation coefficient for the following set of inputs and outputs from a nearly linear system. Instrument was designed for an output equal to twice the input. Full scale is 20. Input 0.50 1.50 2.00 5.00 10.00 Output 0.90 3.05 4.00 9.90 20.50
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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?a) Find the correlation coefficient (keep 4 decimal places) We also have the following partial R output to help answer b) and c) b) What is the predicted weight for a package with a volume of 20 cubic meters (keep 2 decimal places) c) We would like to know if there is a linear relationship between volume and weight. Using the R output above, find the value of the test statistic for this test. (keep 2 decimal places)Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?
- b.Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. c. find the critical valuesWhich of the following is/are true if the coefficient of determination between the response and the predictor variables is 81 percent based on a random sample of size n i. the pearson's sample correlation coefficient is +0.9 ii. this means that 19 percent of the total variation in the response variable remains unexplained by tge simple linear regression model that uses the given predictor variable iii both i and ii iv neither i and iiThere is a relationship between the following variables as y = 1 / (a * x ^ b) (x ^ b: means x over b). a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation. x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10 x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10
- An emergency service wishes to see whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown. Temperature x No. of calls y 68 74 7 4 8 82 88 10 93 11 99 9 Test the significance of the correlation coefficient at alpha = 0.05 13 101 f = Step 1: State the hypotheses. Step 2: Find the critical values. Step 3. Compute the test value. Step 4. Make the decision. Step 5. Summarize the results.1.) Below are cellular data speeds from Sprint and Verizon measured at different airports Sprint: 13.0 30.4 15.2 2.4 2.7 2.1 0.8 1.6 5.6 Verizon: 38.5 55.6 22.4 14.1 23.1 24.5 6.5 21.5 25.7 At a= 0.05 a.) Calculate r and determine if there is linear correlation. State the critical value. b.) If there is linear correlation, find the regression line. If not, skip this step. c.) LAX has Sprint speed of 10.2. Predict Verizon’s speed at LAX. 1a.) r= ____________ Linear? ___________ CV: ____________ b.) ____________________ c.) ___________________Which of the following statements concerning the linear correlation coefficient are always true? I: The value of the linear correlation coefficient always lies between−1 and 1. II: If the linear correlation coefficient for two variables is zero, then there is a strong linear relationship between the variables. III: If the slope of the regression line is negative, then the linear correlation coefficient could be either negative or positive. IV: A linear correlation coefficient of −0.82 suggests a stronger linear relationship than a linear correlation coefficient of 0.62.
- Which of the following is NOT a good reason for including a disturbance term in a regression equation? Select one: a. It captures omitted determinants of the dependent variable b. To allow for errors in the measurement of the dependent variable c. To allow for random influences on the dependent variable d. To allow for the non-zero mean of the dependent variableThe following table shows the magnitude of earthquakes on the Richter scale, x, and the corresponding depth of the earthquakes (in kilometers) below the surface at the epicenter of the earthquake. Find the correlation coefficient of the following pairs of data: x = earthquake magnitude 2.9 4.2 3.3 4.5 2.6 3.2 3.4 y = depth of earthquake (in km) 5 10 11.2 10 7.9 3.9 5.51.Calculate the Pearson correlation coefficient. (you only need to show the values of SSxy, SSx and SSy in the formula, and the value of r. ) 2.Is this Pearson’ r significant at level of αtwo-tail = 0.05? (you only need to show the critical value of r, and the comparison between robt and rcrit.) ID X Y S01 20 190 S02 25 177 S03 30 183 S04 35 153 S05 40 159 S06 45 155 S07 50 130 S08 55 122 S09 60 126 S10 60 105
