Regression Equation, R-squared Value, Intercept

Instructions:
? Write the regression equation
? What does R-squared value tell you?
? What meaning does intercept have?
? Which is warmer, a day with rain or a day without?
? Is KIAH_Precip a good predictor?
? Describe fit of regression

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?