Use for Problems 2 and 3. Scientists examined the activity level of 7 fish at di

Question

Use for Problems 2 and 3. Scientists examined the activity level of 7 fish at different temperatures. Fish activity, y, was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature, x, was measured in degrees Celsius. Using the method of least-squares, the scientists obtained the following information:

b0 = 148.62 b1 = 3.2167 r = 0.954 r2 = 0.910

2. Interpret the estimated slope of the line.

(a) For a one-point increase in temperature, we estimate the fish activity score will decrease by 3.2167.

(b) For a one-point decrease in fish activity score, we estimate the temperature will increase by 148.62.

(c) For a one-point decrease in temperature, we estimate the fish activity score will increase by 3.2167.

(d) For a one-point increase in temperature, we estimate the fish activity score will increase by 3.2167.

3. Give a practical interpretation of r 2 .

(a) 91.0% of the differences in fish activity are caused by differences in temperature.

(b) We estimate temperature to increase by 0.910 for every 1-point increase in fish activity.

(c) We can predict temperature correctly 91.0% of the time using fish activity in a least-squares regression model.

(d) 91.0% of the sample variation in fish activity can be explained by the least-squares regression line.

Please work out clearly.

Thanks

Explanation / Answer

Here the dependent variable is y and the independent variable is x

where y represents the fish activity and x represents the temperature.

1. The slope of the line represents the change(increase or decrease) in the value of y for unit change(increase or decrease) in x.

Here b1=-3.2167. Thus for one unit increase in temperature the fish activity will decrease by 3.2167 units.

2. The value of r2 represents the variation in dependent variable explained by the independent one through the fitted model.

Here r2=0.910.So it can be said that 91.0% of the sample variation in fish activity can be explained by the temperature.

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