Question

Income

($1000s) Household

Size Amount

Charged ($)

89.31 2.00 10985.47

61.08 5.00 9792.97

43.95 4.00 6527.55

55.15 6.00 9708.57

40.39 2.00 6335.20

34.06 3.00 4809.57

86.43 4.00 12314.59

79.49 3.00 10823.38

48.40 2.00 7172.03

46.49 3.00 6996.39

50.68 3.00 7349.23

73.77 5.00 11719.66

34.18 4.00 6062.71

81.64 3.00 9861.66

65.08 4.00 10411.15

41.96 3.00 8169.33

41.48 2.00 6705.15

45.21 3.00 5871.21

48.98 5.00 8627.18

35.70 4.00 6466.99

77.36 2.00 9646.36

79.00 3.00 11910.64

52.03 3.00 7624.06

42.91 3.00 7635.68

38.69 5.00 7955.40

59.49 2.00 6076.57

82.77 2.00 11637.13

9.93 3.00 3911.33

59.54 3.00 6756.73

44.92 3.00 7031.92

33.79 3.00 7777.11

27.66 2.00 5470.17

53.17 3.00 8559.86

35.15 4.00 6306.89

89.46 2.00 10466.76

26.45 5.00 4101.41

89.59 6.00 14962.20

73.96 4.00 12153.59

73.15 4.00 11324.99

56.15 3.00 9704.71

46.57 4.00 9592.53

38.29 5.00 7372.79

34.84 4.00 6708.17

74.27 2.00 8743.04

50.16 4.00 9211.51

85.99 3.00 12318.45

50.82 4.00 9109.05

79.99 3.00 12882.03

68.38 5.00 11310.12

64.42 5.00 11356.01

57.78 3.00 8030.32

50.85 3.00 8905.52

41.35 2.00 5863.35

68.88 4.00 10199.39

87.37 4.00 13589.18

42.15 7.00 8958.60

85.91 3.00 9884.07

79.22 4.00 11881.21

72.59 5.00 11091.60

70.79 3.00 12217.53

65.91 4.00 11661.95

50.88 4.00 6898.00

29.77 4.00 5342.99

82.30 2.00 9685.05

44.81 2.00 6882.08

3.99 1.00 1612.58

57.16 6.00 10069.27

23.25 5.00 8063.88

15.31 3.00 6064.65

72.60 3.00 12132.90

72.53 5.00 11562.23

80.31 1.00 9250.01

43.47 6.00 8147.12

65.82 2.00 10219.37

78.58 4.00 11057.59

37.36 5.00 8690.96

50.86 3.00 7186.18

77.72 3.00 12597.46

73.55 2.00 9859.00

73.87 4.00 10205.59

1) Provide graphical summaries of the data. Comment on your findings.

2) Develop an estimated regression equation, using annual income as the independent variable. Insert Regression equation estimation results here (excluding the ANOVA):

a. Interpret the estimated slope coefficient.

b. Interpret the R-square.

c. Interpret the p-value on the slope.

d. Interpret the 95% confidence interval.

3) Develop an estimated regression equation, using household size as the independent variable. Insert Regression equation estimation results here (excluding the ANOVA):

a. Interpret the estimated slope coefficient.

b. Interpret the R-square.

c. Interpret the p-value on the slope.

d. Interpret the 95% confidence interval.

4) Which of the two models is the better predictor of annual credit card charges? Defend your decision.

5) Provide a scatterplot of the standardized residuals from your chosen best model and comment whether the assumption appear to be met.

Answer 1

Using R

df = read.table("../Documents/creditCardData.txt")
colnames(df )= c("Income","Size","Charged")

#2
model1 <- lm (Charged ~Income , data = df)
summary(model1)

#3
model2 <- lm (Charged ~Size , data = df)
summary(model2)

2) Develop an estimated regression equation, using annual income as the independent variable. Insert Regression equation estimation results here (excluding the ANOVA):

a. Interpret the estimated slope coefficient.

slope = 106.482

if income increases by 1000$, amount charged increases by 106.482$ on average

b. Interpret the R-square.

R^2 = 0.7427

this means 74.27 % of variation in amount charged is explained by this model

c. Interpret the p-value on the slope.

p-value = 0

this means that the slope is significantly different from 0

d. Interpret the 95% confidence interval.

95% confidence interval of slope is (92.3556,120.6085)

3) Develop an estimated regression equation, using household size as the independent variable. Insert Regression equation estimation results here (excluding the ANOVA):

a. Interpret the estimated slope coefficient.

similar to Q2

slope = 502.9

if Household size increases by 1 unit , amount charged increases by 502.9$ on average

b. Interpret the R-square.

R^2 = 0.06136

this means 6.136% of variation in amount charged is explained by this model

c. Interpret the p-value on the slope.

p-value = 0.0267

here p-value < 0.05( alpha)

hence we reject the null hypothesis

we conclude that the slope is significant here too

d. Interpret the 95% confidence interval.

95% confidence interval of slope is (59.50223,946.2219)

4) Which of the two models is the better predictor of annual credit card charges? Defend your decision.

Model 1 is better

as this has much higher R^2