Q5) If the following data set obey equation, i.e. y=a+bx linear regression x 3 4 5 9 11 y 42 38 31 28 29 a) the predicted value of y if x := 12.5 is 24.368 24.379 O 24.452 O 24.542 O none of all above O
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic 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?10) A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-0.767 b=31.009 r2=0.609961 r=-0.781 Use this to predict the number of situps a person who watches 7.5 hours of TV can do (to one decimal place)
- '1) Interpret the following regression line y = 10.50 – 0.18x 2) Interpret the following coefficient of determination r? = 0.69 3) Interpret the following coefficient of correlation r =-0.83If our data were a perfect fit to our regression model, such that y; = ŷ;, we would expect | to be in the CI on p.Q1) Interpret the following regression line y = 10.50 – 0.18x
- Class Activity 5 Q4. Considering the following two distributions, which statement is correct? a) SD of the distribution A is larger than that of distribution B. b) Mode of the distribution A is larger than that of distribution B. c) Range of the distribution A is smaller than that of distribution B. d) Mean of the distribution A is larger than that of distribution B. e) A data item with z-score of -1 falls between 30 to 40 in distribution A. f) A data item with z-score of +1 falls between 10 to 20 in distribution B. A B 10 20 30 40 50 60 70 80 90 100Which of the variables is the indepenent variable and dependent variable for the following question. fit a simple linear regression model to predict latitudes using average monthly range lat= latitudes range= the average monthly range between mean montly maximum and minimum temperatures for a selected set of US cities.Suppose the following regression equation was generated from the sample data of 50 cities relating number of cigarette packs sold per 1000 residents in one week to tax in dollars on one pack of cigarettes and if smoking is allowed in bars: PACKS, = 59682.369232-1108.267218TAX + 176.926159BARS; + eį. BARS 1 if city i allows smoking in bars and BARS; = 0 if city i does not allow smoking in bars. This equation has an R² value of 0.347972, and the coefficient of BARS, has a P-value of 0.133971. Which of the following conclusions is valid? Answer 2 Points Keypad Keyboard Shortcuts According to the regression equation, cities that allow smoking in bars have lower cigarette sales than cities that do not allow smoking in bars. Regardless of whether or not there is a smoking ban, if a city increases its cigarette tax by one dollar cigarette sales will increase by approximately 1108 packs. ○ If there is no cigarette tax in a city that allows smoking in bars, the approximate number of cigarette…
- A random sample of 102 observations is selected to estimate the relationship between the price of a used car (y) and its odometer readings (x). The estimated simple regression line is: ý = 6533 – 0.03x (0.004) where the value 0.004 in bracket is the standard error of the point estimator for the slope in the regression model. Question 15. What percent of the variability of the used car values can be explained using this model? O 60% O 36% O 80% O 64% O 95% O o o o4b) The data shows a systolic and a diastolic blood pressure of certain patients. Find the linear regression equation, using the first variable x (systolic) as the independent variable. Find the best predicted diastolic blood pressure for a patient with a systolic blood pressure (y) reading of 140. What is the correlation coefficient, r? Using a significance level of a = 0.05, is there a significant linear relationship between systolic and diastolic blood pressure? Blood Pressure: Systolic Diastolic 112 125 115 136 143 116 123 124 elimii 70 89 65 90 97 64 SUTT nisinoo aqdM 21.SS bns aqdM 78 ahoqnis erit te zbesqz steb ils to 69 bns ago 20.EI to adimil srit terit sonabilnos 2 nistnoo aqdM 21.SS bnc agdM sgsavs arit ferli mislo a hoqnis orti roqque lovedni sonsbilnos 3028 wolsd insmsisiz tomo artezorio SeqdM 2.55 al 2.SS to sulavadi znistmoodi ezusaed mish ads toqque ton zaob 2.55 to sulsy sdt anistroo ti sausosd mislo ert hoqquz 200b to sulav orit nisinoo ton zoob 11 saussed misbb adi…Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?