Question 456948: I'm having difficulty with several parts of this problem. I've made some headway, but I'm fearful that it is all somewhat off so far. I'm finding this very frustrating. It's a multi-part problem. I'm really trying to learn the reasons behind these questions. Would anyone be willing to help me with the steps of how to get to the conclusions?
It might be supposed that rainy days would tend to be cooler than days without rain, other factors being equal. Furthermore, if that rain is widespread enough to affect more than one reporting station in a city, the effect might be expected to be even more pronounced.
The following output from the Excel Analysis ToolPak, shows a regression analysis on a year of Houston weather data. Precipitation data were collected for George Bush International Airport (KIAH) and for Hobby Airport (KHOU), coded as 1 for precipitation and 0 for no precipitation. These values were used as "binary predictors". The dependent variable is the departure of the daily high temperature from the 30 year normal for the date. So, for example, a day with a high temperature two degrees below normal would be shown as a departure value of -2.0.
Regression Statistics
Multiple R 0.1768
R Square 0.0313
Adjusted R Square 0.0258
Standard Error 6.8608
Observations 360
ANOVA
______________df________SS____________MS________F_______Significance F
Regression_____2________542.19_______271.10____5.7594____0.0035
Residual_______357______16804.16_____47.07
Total__________359______17346.35
_________Coefficients____Standard Error_t Stat__P-value_Lower 95%_Upper 95%
Intercept______ 2.6668___0.4381________ 6.0878__0.0000__ 1.8053___3.5283
KIAH_Precip____-2.3840___1.0423________-2.2873__0.0228__-4.4337___-0.3342
KHOU_Precip____-0.6236___0.9994________-0.6240__0.5331__-2.5890___1.3419
a) Write the fitted regression equation
b) What does the R-squared value tell you?
c) What, if any, meaning does the intercept have?
d) Other things being equal, is the temperature warmer on days with or without rain at KIAH?
e) Does the 95% confidence interval for KIAH_Precip slope give us any confidence that precip vs. no precip at KIAH is an important predictor of temperature?
f) Describe the fit of this regression
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! It might be supposed that rainy days would tend to be cooler than days without rain, other factors being equal. Furthermore, if that rain is widespread enough to affect more than one reporting station in a city, the effect might be expected to be even more pronounced.
The following output from the Excel Analysis ToolPak, shows a regression analysis on a year of Houston weather data. Precipitation data were collected for George Bush International Airport (KIAH) and for Hobby Airport (KHOU), coded as 1 for precipitation and 0 for no precipitation. These values were used as "binary predictors". The dependent variable is the departure of the daily high temperature from the 30 year normal for the date. So, for example, a day with a high temperature two degrees below normal would be shown as a departure value of -2.0.
Regression Statistics
Multiple R 0.1768
R Square 0.0313
Adjusted R Square 0.0258
Standard Error 6.8608
Observations 360
ANOVA
______________df________SS____________MS________F_______Significance F
Regression_____2________542.19_______271.10____5.7594____0.0035
Residual_______357______16804.16_____47.07
Total__________359______17346.35
Variables Coficents____SE------------t Stat__P-value_Lower 95%_Upper 95%
Intercept-------2.6668___0.4381________ 6.0878__0.0000__ 1.8053___3.5283
KIAH_Precip____-2.3840___1.0423________-2.2873__0.0228__-4.4337___-0.3342
KHOU_Precip____-0.6236___0.9994________-0.6240__0.5331__-2.5890___1.3419
==============================================================================
a) Write the fitted regression equation
y = 2.6668-2.3840(KIAH)-0.06236(KHOU)
-------------------------------------------------
b) What does the R-squared value tell you?
R^2 =0.0313 tells you that 3% of the variation in temperature is
explained by the KIAH and KHOU predictors.
-------------------------------------------------
c) What, if any, meaning does the intercept have?
The daily high-temp difference from the 30-year norm is 2.6668 degrees
if we don't consider KIAH and KHOU data.
------------------------------------------------
d) Other things being equal, is the temperature warmer on days with or without rain at KIAH?
Because the coef for KIAH is negative, rain at KIAH indicates a lower temp.
------------------------------------------------
e) Does the 95% confidence interval for KIAH_Precip slope give us any confidence that precip vs. no precip at KIAH is an important predictor of temperature?
Yes because the coef for KIAH is in the 95% CI.
------------------------------------------------
f) Describe the fit of this regression
The fit is pretty weak as seen in the low R-value.
======================================================
Cheers,
Stan H.
|
|
|
