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The sales of a certain product (y) depends on the amounts spent on youtube advertising (x). The following data were collected for n = 15 months. х V 26.52 276.12 53.4 20.64 181.8 216.96 10.44 69 144.24 12.48 11.16 22.2 15.48 8.64 14.16 15.84 10.32 239.76 79.32 257.64 5.76 12.72 10.32 20.88 28.56 11.04 11.64 117 244.92 22.8 Given: Σx = 1950.12; Σy = 221.64; Σx = 390069.749; Σχy = 35534.6352; y2 = 3756.802. The R output obtained from fitting a regression line to the data is shown below. Coefficients: Estimate Std. Error t value Pr>t (Intercept) 8.377735 1.488068 5.630 8.2e-05 *** X 0.049214 0.009228 5.333 0.000136 *** signif. codes: 0 ****' 0.001 ***' 0.01 '*' 0.05.' 0.1''1 Residual standard error: 3.41 on 13 degrees of freedom Multiple R-squared: 0.6863, Adjusted R-squared: 0.6622 F-statistic: 28.44 on 1 and 13 DF, p-value: 0.0001358 3.1 With reference to the above results, show how the following were calculated. 3.1.1 The estimates of the regression coefficients (8.377735; 0.049214). 3.1.2 The residual standard error (3.41). 3.1.3 The standard error of ß(0.009228). (6) 3.1.4 Multiple R-squared (0.6863). 3.1.5 The F-statistic (28.44) for testing the hypothesis that X and Y are not linearly related. BEBEGGE 3.1.6 The 2nd entry under the heading t value (5.333). 3.1.7 The degrees of freedom associated with the F-statistic (1 and 13). 3.2 A plot of the fitted values versus the residuals (from fitting the line to the data) and the results of a Breusch-Pagan test are shown below.