Questions: The scatterplot displays the relationship between the cost of two different Netflix subscription plans for 65 countries of best fit ŷ = -0.94 + 1.38x and a correlation coefficient r = 0.9788. - cost of a premium subscription - cost of a standard subscription (a) In San Marino the cost of a standard subscription is 14.67 and the cost of a premium subscription is 20.32. Calculate t residual for this country. The residual is . Round to the nearest cent. (b) The standard error of the residuals is se = 0.83. What is the best interpretation of this value?

Solution Steps

The cost of a standard subscription is given as $x = \$14.67$. Using the equation of the line of best fit, we can predict the cost of a premium subscription:

$\hat{y} = -0.94 + 1.38x$ $\hat{y} = -0.94 + 1.38(\$14.67)$ $\hat{y} = -0.94 + \$20.2546$ $\hat{y} = \$19.3146$

The residual is the difference between the actual value and the predicted value. The actual cost of a premium subscription in San Marino is $y = \$20.32$.

Residual $= y - \hat{y}$ Residual $= \$20.32 - \$19.3146$ Residual $= \$1.0054$

Rounding the residual to the nearest cent gives $1.01.

Since the residual is positive, the actual cost of the premium subscription in San Marino is $1.01 higher than predicted by the model.

The standard error of the residuals, \(s_e = 0.83\), means that the typical difference between the actual premium subscription costs and the costs predicted by the model is about $0.83.

Final Answer