х 1. Suppose all the necessary assumptions* are met to build a regression model for the dataset in the table (*review wh

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х 1. Suppose all the necessary assumptions* are met to build a regression model for the dataset in the table (*review what the assumptions are needed and how you'd check each one of them). The data and the R output for the model are as follows: Call: y Im(formula y - x) 387 487 361 393 Residuals: 433 546 1 2 3 5 6 29.096 -3.403 -20.714 -20.825 -5.712 21.558 343 333 381 438 Coefficients: 383 470 Estimate Std. Error t value Pr(>ltl) (Intercept) -457.5160 132.9350 -3.442 0.02625 * 2.3654 0.3477 6.803 0.00244 ** 4 х Signif. codes: 0 ****' 0.001 "**' 0.01 "*' 0.05.' 0.1'' 1 Residual standard error: 23.55 on 4 degrees of freedom Multiple R-squared: 0.9205, Adjusted R-squared: 0.9006 F-statistic: 46.28 on 1 and 4 DF, p-value: 0.002439 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) 1 25667.2 25667.2 46.284 0.002439 ** Residuals 4 2218.3 554.6 х Signif. codes: 0 ***** **' 0.001 0.01 0.05.' 0.1'' 1 a) What is the estimated response when the predictor is 574? b) Find the sample correlation between x and y. c) Test if there is a significant linear relationship between the predictor and response.