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?

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?
Transcript text: The scatterplot displays the relationship between the cost of two different Netflix subscription plans for 65 countries of best fit $\hat{y}=-0.94+1.38 x$ 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 $\$$ $\square$ Round to the nearest cent. (b) The standard error of the residuals is $s_{e}=0.83$. What is the best interpretation of this value?
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Solution

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Solution Steps

Step 1: Calculate the predicted value

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

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

Step 2: Calculate the residual

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=$20.32y = \$20.32.

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

Step 3: Round to the nearest cent

Rounding the residual to the nearest cent gives $1.01.

Step 4: Interpret the residual

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

Step 5: Interpret the standard error of the residuals

The standard error of the residuals, se=0.83s_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

(a) The residual is \\(\boxed{\$1.01}\\). This is an overestimate. (b) The typical difference between the actual premium subscription costs and the costs predicted by the model is about $0.83.

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