The following R output is obtained from a multiple linear regression analysis y
ID: 3258178 • Letter: T
Question
The following R output is obtained from a multiple linear regression analysis y = beta_0 + beta_1 x_1 + beta_2 x_2 + elementof, where E(elementof) = 0, Var(elementof) = sigma^2 and observations (x_1i, x_2i, y_i), i = 1, 2, .., n are independent and identically distributed in which we are interested in the effects of temperature (denoted by x_1) and pressure (denoted by x_2) on the rate of reaction (denoted by y) in a reaction chamber. What is your conclusion for the hypothesis test that there is no effect of the temperature on the rate of reaction? What is the estimated regression line for the effect of the temperature and pressure on the rate of reaction? In the context of this problem, if we fix the pressure value to 0 and we increase the temperature 1 unit, how much change do we expect in the rate of reaction? What percentage of the variability in the data is explained by the estimated regression line? What is the predicted value of the rate of reaction when temperature value is 0, and the pressure value is 0?Explanation / Answer
1. H0: There is no effect on the temperature on the rate of reaction
H1: There is effect on the temperature on the rate of reaction
From the output, the p-value of temperature (X1) is 0.037 which is < alpha 0.05, So we reject H0
Thus we conclude that there is effect on the temperature on the rate of reaction.
2. The estimated regression line for the efect of the temperature and pressure on the rate of reaction is
Y = 2.053 + 0.910X1 + 4.844X2
where y is rate of reaction, X1 is effect of the temperature and X2 is pressure
3. In this context, Given X2 = 0 and X1 = 1 i.e. if the temperature 1 unit increase then rate of reaction increases 0.910 units
4. R2 = 0.9815 = 98.15% of variation in the data is explained by the estiamted regression line
5. The predicted value of the rate of reaction when X1 = 0, pressure value X2 = 0 is
Y = 2.053 + 0.910(0) + 4.844(0)= 2.053