A bored statistician (who runs a space heater when it is cold) ran a regression

Question

A bored statistician (who runs a space heater when it is cold) ran a regression predicting the amount of his electric bill from the average temperature of the previous month. The data and results of the linear regression appear below.

1. Is average monthly temperature useful for predicting the statisticians electric bill? Why or why not?

2. What is the estimate of the intercept of the model, and what is its interpretation?

3. What is the estimate of the effect of average monthly temperature, and what is its interpretation?

Tem Bl Tem Bill cm 51 $71.69 34 $77.93 45 $73.82 61 $72.64 32 $77.81 39$74.41 74 $66.62 41 $74.43 35$76.24 77 $7070 43 $78.87 30$80.80 78 $6849 57 $69.48 49$77.64 74 $67.88 66 $70.89 68 $68.70 59 $68.66 72 $70.89 76 $70.23 48 $76.23 72 $71.39 44 $85.13 70 $68.31

Explanation / Answer

1) YES. Both the variables are interrelated,so that first we fit linear regression line of the given data then we can estimate the statistician electic bill by using average monthly temperature

2) b hat is the estimated value of the intercept

interpretation: If 'b' hat is positive,One unit change in averge monthly temperature then statistician electric bill will be increased by 'b' units

If 'b' hat is negative then statistician electric bill will bedecreased by 'b' units

3) it depend on the value of b hat

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