6- Assume that we have two variables A and B and n pair of values for each of them. According to the summary result of linear regression model between A and B obtained from R below, which statement is true? Call: Im (formula = B - A) Residuals: Min 10 Median 30 Маx -16.340 -10.793 -9.653 -8.502 58.325 Coefficients: Estimate std. Error t value Pr (>|t|) (Intercept) 19.6315 20.6457 0.951 0.373 A 9.9609 0.3717 26.800 2.58e-08 *** --- Signif. codes: O **** 0.001 1** 0.01 1** 0.05 '.' 0.1 '' 1 Residual standard error: 26.46 on 7 degrees of freedom Multiple R-squared: 0.9903, Adjusted R-squared: 0.989 F-statistic: 718.2 on 1 and 7 DF, p-value: 2.58le-08 a) It is concluded that A and B variables don't have linear relation with each other. b) P-value for A shows us; variable A is not significant for the model c) 99.03% of the total variation of the values of B in our sample is accounted for by a linear relationship with values of A B is independent value whereas A is dependent value. If we increase A by 1, B will increase by 9.9609 with respect to the fitted regression line d) e)

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 United States gross national product, in trillions of dollars, is given in the table below. Date Gross national product 15.0 2010 2011 15.5 16.2 |2012 | 2013 16.7 (a) Find the equation of the regression line. (Let t be the number of years since 2010. Round regression line parameters to two decimal places.) Gt) = Explain the me aning of its slope. The slope of the line tells us that each year the gross national product increases by trillion dollars. (b) Plot the data points and the regression line. G 17 17 16 16 15 15 14 14 13 13 12 12 1 2 3 1 2 3 G G 17 17 16 16 15 15 14 14 13- 13 12 12 1 2 3 1 2 3 (c) When would you predict that a gross national product of 17.3 trillion dollars would be reached? (Round your answer to two decimal places.) The actual gross national product in 2014 was 17.3 trillion dollars. What does that say about your prediction? • This prediction is accurate. O This prediction is not accurate.

Use RStudio to fit a simple linear regression model to the data below. Please submit a copy of your code and any appropriate output (a photo/screenshot will be sufficient). 300? Is the fitted linear regression model What is the 95% prediction interval for xo = appropriate for this data, and which assumption appears to be violated if not? dataset <- data.frame ( с (294, 247, 267, 358, 423, 311, 450, 534, 438, 688, 630, 709, 627, 1021, 615, 700, 999, 1250, 1015, 850, 980, 1650, 1025, 1200, 1500), у 3 с (30, 32, 37, 44, 47, 49, 56, 62, 68, 80, 84, 88, 97, 97, 100, 106, 109, 112, 117, 128, 130, 135, 160, 180, 210) X = %3D