91Ó°ÊÓ

We are given that A nuclear power plant releases water into a nearby lake every afternoon at $4:51$p.m. and we have to find out the equation of least square regression line.

According to the question,

constant of the equation is the intercept and temperature is the slope,

which results,

$y=-73.64+5.7188x$where x is temperature

Hence, this is the required equation.

We are given with the equation that we have find out in the part (a) and we have to interpret the slope.

From the equation,

we get $slope=5.7188$

Now according to the problem for every $1°$Celsius, the fish are $5.7188m$away from the outflow pipe of the plant.

We are given with the residual plot for the regression and we have to find out if a linear model appropriate for describing the relationship between temperature and distance to the nearest fish.

Now, we will look for any pattern that can violate the residual assumptions but there does not appear any pattern So, the residual assumption is not not violated.

Hence, a linear model is appropriate for describing the relationship between temperature and distance to the nearest fish.

We have to find out if the linear model in part (a) overpredict or underpredict the measured distance from the outflow pipe to the nearest fish found in the water for a temperature of $29°$.

Now, from the equation in Part (a)

which is $y=-73.64+5.7188x$

we will find the value for temperature $29°$

which gives $y=-73.64+5.7188*29=93.2052$

Now check the value of y in the residual plot which gives that

residual is about $-15to-18$.

Hence, the residual is negative the value will also be high.