Part of an environmental health study involved collecting readings on traffic vo

Question

Part of an environmental health study involved collecting readings on traffic volume(vehicles per hour) and carbon monoxide (CO) level (ppm) for each of 28 different times at a metropolitan air quality sampling site. The researchers want know of whether traffic volume and CO are related. a) Write the equation of the regression line. b) Give the P-value and the conclusion for the test of H_0: beta_1 = 0 vs H_A: beta_1 notequalto 0. Your conclusion should contain a description of the relationship between traffic volume and CO, including an interpretation of the slope. c) Predict the CO level for a sampling period with 230 cars. d) Interpret the coefficient of determination in the context of this problem. Bivariate Fit of CO (ppm) By Traffic (cars/hr.) Summary of Fit

Explanation / Answer

Answer

a)

The equation of the regression line is given below.

CO level (ppm) = 7.2523073 + 0.0166241 Traffic (cars/hr)

b)

To determine relationship between traffic volume and CO:

Hypothesis to be tested:

H0: 1 = 0

HA: 1 0

Test statistic = 20.69

P value is < 0.0001.

Since P value is less than level of significance (.01), there is strong evidence to reject the null hypothesis.

Hence we conclude that there is a linear relationship between traffic volume and CO level.

Interpretation of slope: As traffic volume increases by one unit i.e. number of cars increases by one per hour, estimated carbon monoxide level increases by 0.0166241 ppm.

c)

Predicted CO level for sampling period with 230 cars is given below.

CO level (ppm) = 7.2523073 + 0.0166241 Traffic (cars/hr)

CO level (ppm) = 7.2523073 + 0.0166241 * 230

CO level (ppm) = 11.0758503

Hence predicted CO level for sampling period with 230 cars is 11.0758503 ppm.

d)

Coefficient of determination is given by R Square. It is 0.970529. It shows that 97.05% of the variation in response variable CO level is explained by traffic volume and remaining variation is due to randomness.

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