Question

> fm1 <- lm(ascorbic ~ pct.dry + cultB.id + cultC.id, data=lima)

> summary(fm1)

Coefficients: Estimate Std. Error t value Pr(>|t|)

(Intercept) 213.2 16.3 13.1 4.64e-08 ***

pct.dry    -3.9 0.43 -9.1 1.96e-06 ***

cultB.id -6.2 5.53 -1.1 0.290

cultC.id    20.5 5.42 3.8 0.003 **

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Residual standard error: -- intentionally omitted -Multiple R-squared: 0.91, Adjusted R-squared: 0.88 F-statistic: 36.84 on 3 and 11 DF, p-value: 4.956e-06

(c) Determine whether each of the statements below is supported by the multiple regression model above. If the statement is supported, circle “yes”. If the statement is not supported, circle “no”.
YES NO (i) After controlling for differences among the cultivars, there is strong evidence that ascorbic acid content decreases as percent dry weight increases.
YES NO (ii) The estimate of the intercept suggests that lima bean plans of cultivar A have an average ascorbic acid content of 213.
YES NO (iii) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar B is less than the ascorbic acid content of cultivar A.
YES NO (iv) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar C is less than the ascorbic acid content of cultivar A.

Answer 1

> fm1 <- lm(ascorbic ~ pct.dry + cultB.id + cultC.id, data=lima)

> summary(fm1)

Coefficients: Estimate Std. Error t value Pr(>|t|)

(Intercept) 213.2 16.3 13.1 4.64e-08 ***

pct.dry    -3.9 0.43 -9.1 1.96e-06 ***

cultB.id -6.2 5.53 -1.1 0.290

cultC.id    20.5 5.42 3.8 0.003 **

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Residual standard error: -- intentionally omitted -Multiple R-squared: 0.91, Adjusted R-squared: 0.88 F-statistic: 36.84 on 3 and 11 DF, p-value: 4.956e-06

(c) Determine whether each of the statements below is supported by the multiple regression model above. If the statement is supported, circle “yes”. If the statement is not supported, circle “no”.
YES NO (i) After controlling for differences among the cultivars, there is strong evidence that ascorbic acid content decreases as percent dry weight increases.

Answer: Yes. ( the regression coefficient is negative as percent dry weight increases by 1, ascorbic acid content decreases by 3.9.

YES NO (ii) The estimate of the intercept suggests that lima bean plans of cultivar A have an average ascorbic acid content of 213.

Answer: No (213 is average ascorbic acid content of A when percent dry is 0)

YES NO (iii) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar B is less than the ascorbic acid content of cultivar A.

Answer: Yes ( the regression coefficient for cultivar B is negative, ascorbic acid content is less for B)

YES NO (iv) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar C is less than the ascorbic acid content of cultivar A.

Answer:No ( the regression coefficient for cultivar c is positive, ascorbic acid content is more for C)