21. Calculate the Pearson Correlation Coefficient (r): (SHOW YOUR WORK)
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JUST QUESTION 21 PLEASE
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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 regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). yy^=a+bxa=-1.218b=0.171 (b) Which is a possible value for the correlation coefficient, r? (c) If a country increases its life expectancy, the happiness index will increase or decrease ? (d) If the life expectancy is increased by 5 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 59 years. Round to two decimal places.this is date for Colon Cancer New Cases 2017 y1y1=2609.58x2x2-971041 corr(x2y1)(x2y1)=0.988 Could you tell us what your variables in your equation represent for your situation? How do you determine if there is a strong or weak linear correlation from the correlation coefficient? How do you determine if it is positive or negative?
- When you solve and get an r value for the correlation coefficient, what information is revealed by this value?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. The Gross Horsepower of a car can influence the mileage of the car. A random sample of 32 different cars’ Gross Horsepower and mileage (Miles/gallon) is collected. From the data, suppose you got the following results: Pearson’s correlation coefficient: -0.90 The fitted regression line: Ŷ = 30. 10 − 0. 07 X d. Find the value of R2 and comment. e. From the fitted model find the values of Y for given values of X as 110. How do you interpret this value?