Exercise and diet are common factors that affect diabetic symptoms and their nee

Question

Exercise and diet are common factors that affect diabetic symptoms and their need for insulin. A study done at a region hospital collected data from diabetic patients for one month on their daily caloric intake and blood sugar levels; the data is below. Compute the correlation coefficient r = and the linear regression line for the data set: y = The y-intercept of this line tells you the predicted is zero. The slope of this line tells you that as the goes up by 1, the is predicted to (go up/go down) by Using the equation determine the residual for an individual taking in 2000 calories. Determine the residual for this point: What is the predicted blood glucose level of a diabetic with a daily caloric intake of 1750 calories?

Explanation / Answer

take x as calories intake

y as blood glucose

Run Regression in excel

The following is the output obtained

correlation coefficient is

r=0.587

regression equation is

y=50.071+0.030x

slope=0.030

y intercept=50.071

y intercept represent the value of y when the independent x=0

since slope positive

as x goes by 1

the y hat is go up by 0.030

residual=y-yhat

given x =2000

y=98

y hat is iobtained by substituting x=2000 in regression eq

y hat=50.071+0.030x

=y=50.071+0.030(2000)

=110.071

Residual=observed-predicted

=98-110.071

=-12.071

residual for the point=-12.071

REST OF THE QUESTIONS POST SEPERATELY

SUMMARY OUTPUT Regression Statistics Multiple R 0.586683 R Square 0.344197 Adjusted R Square 0.289547 Standard Error 16.34806 Observations 14 ANOVA df SS MS F Significance F Regression 1 1683.248 1683.248 6.298188 0.027427 Residual 12 3207.109 267.2591 Total 13 4890.357 Coefficients Standard Error t Stat P-value Lower 95% Intercept 50.07051 25.76161 1.943609 0.075767 -6.05922 x 0.03008 0.011986 2.509619 0.027427 0.003965 RESIDUAL OUTPUT Observation Predicted y Residuals 1 96.69401 -3.69401 2 99.70198 -3.70198 3 101.206 -0.20596 4 102.7099 0.290053 5 103.4619 41.53806 6 110.2299 -12.2299 7 116.2458 -15.2458 8 117.7498 -9.74979 9 119.2538 -7.25377 10 119.2538 -10.2538 11 123.7657 -11.7657 12 124.6681 0.331888 13 125.2697 6.730294 14 132.7896 25.21037

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