The R script for the linear model and the nonlinear quadratic model .


The following code did the regression calculations and graphing for the Regression Example 1’s solution. You can copy and paste the code into R and it should run without modification. You can download R for free from  R  https://www.r-project.org/ or you can copy and paste the code into a free online R compiler such as: rextester   https://rextester.com/l/r_online_compiler or JDOODLE  https://www.jdoodle.com/execute-r-online

 

# R script for regression examples with Latex
# models y = mx and y = ax^2
RegressionModel = "L";   #"L" = linear model y = mx; "P" = parabolic model y = ax^2

#( -3, 0), (-5,2) Data from Regression HW problem
x = c(-3,-5);
y = c(0, 2);

# Compare your own "guess" of "m" or "a" to the regression "m" or "a".
#---------------------------------------------------------------------
CompareModel = "N"     # "Y" or "N". If "Y", competing model graphed and its SSE calculated.
Guess_m_a = .5;      # enter numerical value for m or for a. Default is .5.

# DO NOT CHANGE ANYTHING BELOW HERE!!!!!!!!!!!
#----------------------------------------------
ShowDeviateBars = "Y"; # "Y" or "N"
GraphPaper = FALSE; #TRUE = prints graph paper; FALSE = plots regression line
ErrorString = "";
CompareModelsString = "Thank you for using R.";
By = 1
#------------------------------------------------------------
if(RegressionModel == "P")
{ f = function(x){x^2;};
a = sum(y*f(x))/sum(f(x)^2); a_3 = round(a,3);
yxx = y*x^2;
xxxx = x^4;
errors = y - a_3*f(x);
errors2 = round(errors^2,3);
SSE = sum( (y - a_3*f(x))^2 ); SSE3 = round(SSE,3); # SSE;
a3x2 = a_3*x^2;
df1 = data.frame(x,y, yxx, xxxx, a3x2, errors, errors2); # df1;
if(ShowDeviateBars == "Y"){ErrorString = "\nErrors shown in red. SSE = ";}
mainTitle = paste("Data points with regression curve y = ", toString(a_3), "x^2",ErrorString, toString(SSE3));
if(GraphPaper){mainTitle = "(d) Plot the data points and the regression curve y = a x^2";};
}
if(RegressionModel == "P"){
sum_yxx = sum(yxx);
sum_xxxx = sum(xxxx);
SSE_sum_errors2 = sum(errors2);
df2 = data.frame(sum_yxx, sum_xxxx, a_3, SSE_sum_errors2); #df2;
}
#------------------------------------------------------------
#------------------------------------------------------------
if(RegressionModel == "L")
{ f = function(x){x;};
a = sum(y*f(x))/sum(f(x)^2); a_3 = round(a,3);
yx = y*x;
xx = x^2;
errors = y - a_3*f(x);
errors2 = round(errors^2,3);
sum_yx = sum(yx); # sum_yx;
sum_xx = sum(xx); # sum_xx;
SSE = sum( (y - a_3*f(x))^2 ); SSE3 = round(SSE,3); # SSE;
mx = a_3*x;
df1 = data.frame(x,y, yx, xx, mx, errors, errors2); # df1;
if(ShowDeviateBars == "Y"){ErrorString = "\nErrors shown in red. SSE = ";}
mainTitle = paste("Data points with regression line y = ", toString(a_3), "x",ErrorString, toString(SSE3));
if(GraphPaper){mainTitle = "(d) Plot the data points and the regression line y = m x";};
}
if(RegressionModel == "L"){
sum_yx = sum(yx);
sum_xx = sum(xx);
SSE_sum_errors2 = sum(errors2);
df2 = data.frame(sum_yx, sum_xx, a_3, SSE_sum_errors2); # df2;
}
#------------------------------------------------------------

# Range Calculatins to center graph paper
#------------------------------------------------------------
RangeY = max(y, a_3*f(x),0 ) - min(y, a_3*f(x), 0); # RangeY ;
RangeX = max(x,0) - min(x,0); # RangeX ;
if(RangeX < RangeY){
Ymin = round(min(y,0, a_3*f(x)) - 1,0); # Ymin;
Ymax = round(max(y,0, a_3*f(x)) + 1,0); # Ymax;
RangeYnew = Ymax - Ymin;
Xmin = round(min(x,0) - (RangeYnew - RangeX)/2, 0); # Xmin;
Xmax = round(max(x,0) + (RangeYnew - RangeX)/2, 0); # Xmax;
}
if(RangeY < RangeX){
Xmin = min(x,0) - 1;
Xmax = max(x,0) + 1;
Ymin = round(min(y,0, a_3*f(x)) - (RangeX - RangeY)/2,0);
Ymax = round(max(y,0,a_3*f(x)) + (RangeX - RangeY)/2,0);
}
# Ymin;
# Ymax;
# Xmin;
# Xmax;

# Plot graph paper
#------------------------------------------------------------
plot(1, type="n", xlab="", ylab="",
xlim=c(Xmin, Xmax ), ylim=c(Ymin , Ymax ), asp=1 , main = mainTitle );
arrows(0,Ymin, 0, Ymax, length = 0.25, angle = 30,
col = "black", lty = 1, lwd = 3);
arrows(Xmin,0, Xmax, 0, length = 0.25, angle = 30,
col = "black", lty = 1, lwd = 3)

xSeq = seq(Xmin, Xmax, by = By);
lenxSeq = length(xSeq);
for(i in 1:lenxSeq){
lines( c(xSeq[i], xSeq[i]), c(Ymin, Ymax), col = "blue")
}
ySeq = seq(Ymin, Ymax, by = By);
lenySeq = length(ySeq);
for(i in 1:lenySeq){
lines( c(Xmin, Xmax), c(ySeq[i], ySeq[i]), col = "blue")
}
#------------------------------------------------------------
if(GraphPaper == FALSE){
if(ShowDeviateBars == "Y"){
for(i in 1:length(x)){lines( c(x[i],x[i]), c( y[i], a_3*f(x[i]) ), col = "red", lwd = 4);};
}
points( x, y, pch = 20, cex = 3); # data
xSeq = seq(Xmin, Xmax, by = By/10);
lines( xSeq, a_3*f(xSeq), lwd = 4); # regression line
}
# ------------------
if(RegressionModel == "L"){modelStrR = paste("y = ", toString(a_3),"x", sep = "");};
if(RegressionModel == "P"){modelStrR = paste("y = ", toString(a_3),"x^2", sep = "");};
CompareModelsString = paste("The regression curve ",
modelStrR,
", drawn in black, has SSE = ",
toString(SSE3),
". Thank you for using R.",
sep = "");
# ------------------
if(CompareModel == "Y"){lines(xSeq,Guess_m_a*f(xSeq), lwd = 4, col = "blue");
SSE_compare = sum( (y - Guess_m_a*f(x))^2 );
if(RegressionModel == "L"){modelStrG = paste("y = ", toString(Guess_m_a),"x", sep = "");
modelStrR = paste("y = ", toString(a_3),"x", sep = "");};
if(RegressionModel == "P"){modelStrG = paste("y = ", toString(Guess_m_a),"x^2", sep = "");
modelStrR = paste("y = ", toString(a_3),"x^2", sep = ""); };
CompareModelsString = paste("The regression curve ",
modelStrR,
", drawn in black, has SSE = ",
toString(SSE3),
". Your model ",
modelStrG,
", drawn in blue, has SSE = ",
toString(SSE_compare),
".", sep = "");
};
CompareModelsString;
# ------ display data.frames of regression calculations
df1;
df2;
#End of R script

 

---