Question

The accompanying table shows the net sales (in billions of dollars), total assets (in billions of dollars), and shareholder's equities (in billions of dollars) for a company for five years.

Calculate r2adj and determine the percentage of the variation in y that can be explained by the relationships between variables according to

r2adj.

Compare this result with the one obtained using r2.

Shareholder's equity, y 62.8 64.5 71.6 69.6 70.7

Net sales, x1 370.1 402.5 405.7 416.1 443.7

Total assets, x2 162.7 160.5 174.8 181.2 191.7

Answer 1

Adjusted R-squared: 0.3725

Multiple R-squared: 0.6862

******************************************************** R OUTPUT for reference*********************************************************

Call:
lm(formula = survey_data$Shareholder_y ~ survey_data$Net_Sales_x1 +
survey_data$Total_Aassets_x2)

Residuals:
1 2 3 4 5
-1.6871 -0.4723 3.6913 0.1217 -1.6536

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21.57295 24.01397 0.898 0.464
survey_data$Net_Sales_x1 0.02848 0.11696 0.244 0.830
survey_data$Total_Aassets_x2 0.19897 0.23859 0.834 0.492

Residual standard error: 3.118 on 2 degrees of freedom
Multiple R-squared: 0.6862,   Adjusted R-squared: 0.3725
F-statistic: 2.187 on 2 and 2 DF, p-value: 0.3138

/***************************************** R CODE ********************************/

survey_data<-read.csv("D:/Sourav/Chegg Question and Answer/R_Programming/Q_1/Data.csv", header=TRUE)
survey_data

model <- lm(survey_data$Shareholder_y ~ survey_data$Net_Sales_x1+survey_data$Total_Aassets_x2)
summary(model)

model$coef

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