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Wesley thinks his heartrate will increase as he increases his running speed. To see if this...

Wesley thinks his heartrate will increase as he increases his running speed. To see if this relationship exists, he records eight different speeds and models it with a scatterplot and regression output.

A scatterplot is shown with the x axis labeled Speed, miles per hour, and the y axis labeled Pulse, beats per minute. The points on the graph increase from 0.75 and 72 to 4.1 and 131.
Regression Statistics
Multiple R 95.70928%
R Square 91.60266%
Adjusted R Square 90.20310%
Standard Error 6.513645838
Observations 8
df SS MS F
Regression 1 2,776.934507 2,776.934507 65.45116
Residual 6 254.5654926 42.4275821
Total 7 3031.5
Coefficients Standard Error t Stat p-Value
Intercept 63.06927886 5.643282415 11.17599195 3.06E-05
Speed 18.57636597 2.296159651 8.090189183 0.000191
Coefficients Standard Error t Stat p-Value
Intercept 63.06927886 5.643282415 11.17599195 3.06E-05
Speed 18.57636597 2.296159651 8.090189183 0.000191

Part A: Write the equation of the regression line using the regression output.

Part B: What do the slope and intercept parameters mean using the context of the problem?

Part C: Compute the margin of error that Wesley should use if he wants to provide a 98% confidence interval for the slope. Assume that conditions for inference are satisfied.

math   Statistics-And-Probability   
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Answer #1

A.
Regression equation is
ycap = 63.0693 + 18.5764x

B.
Here slope = 18.5764, indicates the increase in heart rate for every 1 unit increase in the speed of running.
intercept = 63.0693 indicates the base heart-rate, this means even if someone is not running the heart-rate would be 63.0693

C.
For 98%, t- value = 2.998

ME = t*SE
ME = 2.998*18.5764 = 55.6920

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