Question

Listed below are the heights In Inches and weights in pounds of 10 Super Models. Models of this type are typically tall and thin. From the given pairs of data, your task is to do the following: 1) Construct a Seatter Diagram 2) Determine the Line of Regression (9 = bo + bx) 3) Calculate the Coefficient of Correlation (r) 4) Make a Prediction You must show your work to get full credit. Round all answers to 2 decimal places Height (*) 77 686 76 76 66 66 6 7 Weight (9) 131 119 126 12 18 114 108 12 12 116 SCATTER DIAGRAM 130 70 69 71 - 65 66 67 Height

Answer 1

1. Scatter Diagram:

Scatter Diagram Weight 106 64 65 66 67 70 71 72 73 68 69 Height

Scatter Diagram Weight 106 64 65 66 67 70 71 72 73 68 69 Height

2. Line of Regression: y-hat = 29.8720 + 1.2711*x

so b0 = 29.8720 and b1= 1.2711

3. Coefficient of correlation (r) = 0.6171

Correlation Cov(x,y) vrea). vey) = (x - x) (ai-y) 3 (4-5)? Ž (7: -3)?

4. Make a prediction:

For height(x) 75, weight will be = 29.8720 + 1.2711 * 75 = 125.2045

/******************************************* R Output *****************************************8/

survey_data<-read.csv("D:/Sourav/Chegg Question and Answer/R_Programming/Q_1/Data.csv", header=TRUE)
> survey_data
Height_x Weight_Y
1 71 121
2 68 119
3 67 120
4 70 122
5 70 118
6 66 114
7 68 108
8 72 122
9 65 112
10 70 116
> model <- lm(survey_data$Weight_Y ~ survey_data$Height_x)
> summary(model)

Call:
lm(formula = survey_data$Weight_Y ~ survey_data$Height_x)

Residuals:
Min 1Q Median 3Q Max
-8.3102 -0.7636 0.4187 2.2364 4.9610

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 29.8720 39.3880 0.758 0.4700
survey_data$Height_x 1.2711 0.5731 2.218 0.0573 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.891 on 8 degrees of freedom
Multiple R-squared: 0.3808,   Adjusted R-squared: 0.3034
F-statistic: 4.92 on 1 and 8 DF, p-value: 0.05734

PLEASE LET ME KNOW IF YOU HAVE ANY DOUBTS. THANKS!!