The data was inputed as an R data.frame called lab1. With the column names xcoord, ycoord and obs. A spatial map of the data is shown below with the size of each points representing the observation.

Spatial Map of Lab 1 Data

A multiple linear regression model is built.

## 
## Call:
## lm(formula = obs ~ xcoord + ycoord, data = lab1)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -5.562 -3.325 -1.225  2.650  7.513 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  10.4375     3.7032   2.819 0.014506 *  
## xcoord        5.2250     0.9987   5.232 0.000162 ***
## ycoord        2.0750     0.9987   2.078 0.058109 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.466 on 13 degrees of freedom
## Multiple R-squared:  0.7091, Adjusted R-squared:  0.6644 
## F-statistic: 15.85 on 2 and 13 DF,  p-value: 0.0003268

The summary of model shows both X and Y coordinate is significant in the linear regression model. The adjusted R-square is \(.6644\), which means there are quite strong linear correlation between coordinates and response. The predicted value under this model at \((2.5, 2.5)\) is 28.6875. This is quite close to the response of the points near it \((21, 24, 29, 27)\). The following plot added the unobserved data onto the previous map.

Spatial Map of Observed and Unobserved Data