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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?The observations of yields (y) of a chemical reaction taken at various temperatures (x) were recorded in the following table:a) Calculate the correlation coefficient and test the significance at 5% probability;b) Find the simple linear regression equation;c)Calculate the coefficient of determination.d) What is the expected efficiency of the chemical reaction for a temperature of 270 °C?You have run a security characteristic line for a company's stock. The variance is .20. The variance of the error or residuals is .07. The variance of the market is .18. What is the beta? I arrived at .722. And what is the R-square of your regression?
- 1. Explain the purpose or use of the following:a. Linear regression equationb. Correlation coefficient.Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient.
- With the help of the observations of X and Y variables;a) Estimate and graph the regression equation.b) Estimate the Y value for X = 9.c) Calculate the correlation coefficient. Determine the direction and degree of this relationshipd) Test the hypothesis that p is not different from zero for α = 0.01 and α = 0.05 significance level.1a. Develop an estimated regression equation for these data. 1b. Compute the residuals and standardized residualsUsing the regression table I created, how should I perform a T-test for the predictors and assuming the Normality, Homoscedasticity, Independence of observations are satisfied?
- Find the slope of regression line, y-intercept of regression line, coefficient of determination (r^2), and the linear correlation coefficient (r)An experiment was carried out to observe the relationship between the time (Y) necessary for a vendor to supply a showcase in a store with sodas, and the boxes of product supplied (X), the information recorded is as follows (image) From the data: a. Get the fitted simple linear regression model b. Construct a scatterplot and discuss the result c. perform the analysis of variance. ThanksFor a linear regression for a sample of n=20 pairs of X and Y values. What is the value of the degrees of freedom for the predicted portion of the Y-score variance, MSregression?