#load the library and import the data set
##-------------- Shoe Size and Height ---------------##
library(readxl)
shoe = read_excel("C:\\Users\\user\\Downloads\\Shoe.xlsx")
shoe
## # A tibble: 28 x 3
## shoe_size height gender
## <dbl> <dbl> <chr>
## 1 6.5 66 F
## 2 9 68 F
## 3 8.5 64.5 F
## 4 8.5 65 F
## 5 10.5 70 M
## 6 7 64 F
## 7 9.5 70 F
## 8 9 71 F
## 9 13 72 M
## 10 7.5 64 F
## # ... with 18 more rows
## Find the correlation between shoe size and height of the respondents.
## Use 0.05 level of significance.
scatter.smooth(x=shoe$shoe_size,
y=shoe$height,
main="Scatter Plot")
cor(shoe$height, shoe$shoe_size)
## [1] 0.7766089
## Based on the value of r which is 0.7766089 , the height and shoe size has a
# positive relationship. This means that as the shoe size increases
# the height increases.
# Calculate the p-values. Interpret the result.
linearMod_shoe_size <-lm(height~shoe_size, data=shoe)
linearMod_shoe_size
##
## Call:
## lm(formula = height ~ shoe_size, data = shoe)
##
## Coefficients:
## (Intercept) shoe_size
## 54.112 1.536
summary(linearMod_shoe_size)
##
## Call:
## lm(formula = height ~ shoe_size, data = shoe)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1722 -1.5712 0.1325 1.8461 4.2549
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54.1123 2.3524 23.003 < 2e-16 ***
## shoe_size 1.5365 0.2444 6.286 1.18e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.604 on 26 degrees of freedom
## Multiple R-squared: 0.6031, Adjusted R-squared: 0.5879
## F-statistic: 39.51 on 1 and 26 DF, p-value: 1.183e-06
# Linear regression model: Y(hat) = 54.11 + 1.54 * X
## Based on the of p-value which is 0000001.183 , the linear regression model
# is statistically significant since the p-value is less than 0.05. Also, we can
# conclude that shoe size has a connection with height. Therefore,
# we can use the model to predict the height of a person.
##-------------- Shoe Size and Height ---------------##
#load the library and import the data set
orions = read_excel("C:\\Users\\user\\Downloads\\Orions.xlsx")
orions
## # A tibble: 11 x 2
## age price
## <dbl> <dbl>
## 1 5 85
## 2 4 103
## 3 6 70
## 4 5 82
## 5 5 89
## 6 5 98
## 7 6 66
## 8 6 95
## 9 2 169
## 10 7 70
## 11 7 48
## Set up scatter plot
scatter.smooth(x=orions$age,
y=orions$price,
main="Scatter Plot")
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
cor(orions$age,orions$price)
## [1] -0.9237821
##a. Determine the regression equation for the data.
linearMod_price <-lm(price~age, data=orions)
linearMod_price
##
## Call:
## lm(formula = price ~ age, data = orions)
##
## Coefficients:
## (Intercept) age
## 195.47 -20.26
## The regression equation Y(hat) = 195.47 - 20.26 * X
##b. Graph the regression equation and the data points.
scatter.smooth(x=orions$age,
y=orions$price,
main="Scatter Plot")
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## pseudoinverse used at 5
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## neighborhood radius 1
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric = FALSE, :
## There are other near singularities as well. 1
##c. Describe the apparent relationship between age and price of Orions
## Based on the graph, the age and price of orions has a negative relationship.
## This means that, as age increases the price of orions decreases.
##d. Interpret the slope of the regression line in terms of prices for Orions.
## Since the slope is -20.26, this implies that when the age increases by 1
## the price decreases by 20.26.
##e. Use the regression equation to predict the price of a 3-year old Orion and 4-year-old Orion.
price_3_year_old = 195.47 - 20.26 * 3
price_3_year_old
## [1] 134.69
# Therefore, the price of a 3-year old orion is 134.69
price_4_year_old = 195.47 - 20.26 * 4
price_4_year_old
## [1] 114.43
# Therefore, the price of a 3-year old orion is 114.43