Answer :
Since the p-value is less than the level of significance, the correlation is significant. Therefore, the linear correlation is strong.
x y 70 69.5 51.9 -21.7 58.1 39.1 67.4 74.9 95 156.2 70.7 97.6 62.9 89 50.4 16.8 60.9 37.4 49 29.1 61.4 59.6 60.3 35.1. Correlation coefficient (r) = 0.819 correct to three decimal places.
Coefficient of determination (r²) = 0.671 correct to three decimal places. Therefore, the proportion of the variation in y that can be explained by the variation in the values of x is 67.1%. Each value should be correct to three decimal places. Therefore, the regression line equation is y = 0.976x - 21.965. y = 0.976(49.2) - 21.965 = 25.534. Therefore, the predicted response value is 25.5. This value represents the average of the response variable (y) that is expected to be obtained from a value of 49.2 as the explanatory variable x. Use a significance level of α = 0.05 to evaluate the strength of the linear correlation.
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