Question

A state fisheries commission wants to estimate the number of bass caught in a given lake during a season in order to restock the lake with the appropriate number of young fish. The commission could get a fairly accurate assessment of the seasonal catch by extensive "netting sweeps" of the lake before and after a season, but this technique is much too expensive to be done routinely. Therefore, the commission samples a number of lakes and record the seasonal catch (thousands of bass per square mile of lake area) and size of lake (square miles). A simple linear regression was performed and the following Routput obtained. (Intercept) size Estimate Std. Errort 2.5463 0.4427 0.0667 0.3672 value 5.7513 0.1818 Pr(>t) 0.0000 0.8578 Which of the following is the correct interpretation of the slope? Seasonal catch for a lake that is O square miles in area is predicted to be 2,546.3 per square mile of lake area. Seasonal catch for a lake that is 0 square miles in area is predicted to be 66.7 per square mile of lake area. Seasonal catch is predicted to increase by 1,000 for every increase in lake area of 0.0667 square miles. As lake area increases by 1 square mile, seasonal catch is predicted to increase by 66.7, on average. As lake area increases by 1 square mile, seasonal catch is predicted to increase by 2,546.3, on average.

Answer 1

Answer:-

From the above R output,

The simple linear regression model is written by

y = bo + b1 x

Where bo is intercept term and b1 is slope term, x is size of lake ( square miles) , y is seasonal catch ( thousands of bass per square miles of a lake area)

y = 2.5463 + 0.0667 x

bo = 2.5463 and b1= 0.0667

The correct interpretation of the slope is

As lake area is increases by 1 square mile, season catch is predicted to increase by 66.7 on average.

statement 4 is correct.

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