Do your estimates of the slope and intercept parameters have

Do your estimates of the slope and intercept parameters have meaningful interpretations in the context of this question? If so provide interpretations in this context. If not, explain why not.

Use data below:

John believes that as he increases his walking speed, his pulse rate will increase. He wants to model this relationship. John records his pulse rate, in beats per minute (bpm), while walking at each of seven different speeds, in miles per hour (mph). A scatterplot and regression output are shown below.

Solution

John is correct in his belief.

The slope coefficient of speed of the regression equation is positive and is statistically significnatly determining the pulse rate as it has a P value < 5% level of significance.

A statistically significantly positive intercept implies that even when the speed is zero, pulse rate is positive and significant, which is obvious as the person is living even when he is stationary.

A high R² of 98.7% implies that the model explains 98.7% of the variation in pulse rate, by the speed of walking. Hence, the model explains the variation well.

Also, the analysis of variance concludes that the P value for F stat is close to zero, hence, the regression performed is significant.