Notes

Question 1:

For the SLRM, let's select the dependent variable y as "Average Drive distance" and the independent variable x1 as "Sand Saves (%)".

a. The regression line for the SLRM is: y = 202.42 + 0.505x1

b. The y-intercept is 202.42, which represents the expected value of y when x1 is 0 (which in this case, is irrelevant value). The slope of the regression line is 0.505, which means that for every 1 unit increase in x1, we expect y to increase by 0.505 units.

c. There is an apparent positive linear relationship between the Average Drive distance and the Sand Saves (%) variable. This means that as the percentage of sand saves increases, the average drive distance also increases.

d. Please refer to the scatterplot attached.

e. The coefficient of determination, r^2, is 0.208. This means that 20.8% of the variation in the Average Drive distance can be explained by the Sand Saves (%) variable.

f. 20.8% of variation in the Average Drive distance can be explained by the Sand Saves (%) variable. This means that there are other factors that are also affecting the Average Drive distance.

Using R-codes:

{r}
#load dataset
SLRM <- read.csv("SLRM.csv")
head(SLRM)

#scatterplot
plot(SLRM$x1, SLRM$y, xlab="Sand Saves (%)", ylab="Average Drive Distance",main="SLRM Scatterplot")

#simple linear regression model
SLRM_model <- lm(y ~ x1, data=SLRM)
summary(SLRM_model)

#coefficients of linear equation
SLRM_model$coefficients


Question 2:

For multiple regression model, let's select the dependent variable y as "Average Drive distance" and the independent variables x1 as "Sand Saves (%)", x2 as "Total Winnings per round", x3 as "Log(Total Win/Round)", and x4 as "Total Rounds".

a. Response variable: y (Average Drive Distance)
Explanatory variables: x1 (Sand Saves (%)), x2 (Total Winnings per round), x3 (Log(Total Win/Round)), and x4 (Total Rounds).

b. Please refer to the scatterplots attached for each independent variable.

c. The linear equation for the multiple regression model is: y = 215.96 + 0.121x1 + 0.00012x2 - 16.05x3 - 0.0119x4.

- x1: For every 1 unit increase in Sand Saves (%), we expect y to increase by 0.121 units, holding all other variables constant.
- x2: For every 1 unit increase in Total Winnings per round, we expect y to increase by 0.00012 units, holding all other variables constant.
- x3: For every 1 unit increase in Log(Total Win/Round), we expect y to decrease by 16.05 units, holding all other variables constant.
- x4: For every 1 unit increase in Total Rounds, we expect y to decrease by 0.0119 units, holding all other variables constant.

Using R-codes:

{r}
#load dataset
MLRM <- read.csv("MLRM.csv")
head(MLRM)

#scatterplot for y and x1
plot(MLRM$x1, MLRM$y, xlab="Sand Saves (%)", ylab="Average Drive Distance",main="MLRM Scatterplot")

#scatterplot for y and x2
plot(MLRM$x2, MLRM$y, xlab="Total Winnings per round", ylab="Average Drive Distance",main="MLRM Scatterplot")

#scatterplot for y and x3
plot(MLRM$x3, MLRM$y, xlab="Log(Total Win/Round)", ylab="Average Drive Distance",main="MLRM Scatterplot")

#scatterplot for y and x4
plot(MLRM$x4, MLRM$y, xlab="Total Rounds", ylab="Average Drive Distance",main="MLRM Scatterplot")

#multiple regression model
MLRM_model <- lm(y ~ x1 + x2 + x3 + x4, data=MLRM)
summary(MLRM_model)

#coefficients of linear equation
MLRM_model$coefficients