Question

it turns out this regression equation accounts for 66.1% of the variability in number of wins.

1. in the space below, describe the relationship between total number of runs allowed and total number of wins.

as more runs are allowed, the fewer wins it gets.

1. as total number of runs allowed increases by __________, we predict total number of wins to go down by ________.

Explanation:

Step1: Analyze the scatter plot trend

The scatter plot has a negative linear trend (downward - sloping line). To find the slope (rate of change), we can use two points on the line. Let's take the left - most point (500, 100) and a point further right, say (850, 60) (approximate from the graph).

Step2: Calculate the slope

The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x_1 = 500,y_1 = 100,x_2 = 850,y_2 = 60$. Then $m=\frac{60 - 100}{850 - 500}=\frac{- 40}{350}\approx-\frac{4}{35}\approx - 0.114$. But a more intuitive way: from $x = 500$ to $x = 850$ (an increase of 350 runs), $y$ decreases from 100 to 60 (a decrease of 40 wins). So the rate is $\frac{40}{350}=\frac{4}{35}\approx0.114$ wins per run decrease. But if we take a smaller interval, say from $x = 500$ to $x = 600$ (increase of 100 runs), the $y$ - value at $x = 500$ is 100, at $x = 600$ (approximate) is 90. So the decrease in wins is $100 - 90 = 10$ when runs increase by 100. So the relationship is: as runs allowed increase by 100, wins decrease by 10 (approximate, based on the linear trend in the graph).

Answer:

As total number of runs allowed increases by 100, we predict total number of wins to go down by 10 (answers may vary slightly based on the exact points chosen on the regression line, but this is a reasonable approximation from the graph's trend).